Pith. sign in

REVIEW 3 major objections 5 minor 160 references

Advanced Techniques in Stability Analysis of Trans-Neptunian Objects

T0 review · 3 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read The Kuiper Belt's present-day structure is a fossil record of the proto-planetary disk and Neptune's migration, decoded through hybrid machine-learning-plus-Hamiltonian frameworks.

desk verdict A useful but numerically inconsistent review of TNO stability methods; worth refereeing once the diffusion-coefficient conflict is fixed. read the letter →

arxiv 2607.13629 v1 pith:Z65QYOJS submitted 2026-07-15 astro-ph.EP astro-ph.IMnlin.CD

Tamás Kovács This is my paper · ORCID
classification astro-ph.EPastro-ph.IMnlin.CD
keywords trans-NeptunianobjectsKuiperBeltmean-motionresonancessecularchaoticdiffusionstabilityindicatorsplanetarymigrationmachinelearning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper is a review that tries to establish that the trans-Neptunian region (30–50 AU) is not a random debris disk but a structured archive: the resonant populations trapped with Neptune, the cold/hot classical split, the narrow 44-AU 'kernel', and the scattered and detached objects together record the initial conditions of the proto-planetary disk and the migration history of the ice giants. It argues that the quantitative backbone for reading this record is the family of chaos indicators—Lyapunov exponents, MEGNO, SALI/GALI, frequency map analysis, entropy and recurrence-based measures—supplemented by an anomalous-diffusion framework that classifies sub- and superdiffusive orbital transport. The forward-looking thesis is that the most promising path forward is hybrid dynamical–statistical frameworks anchored to Hamiltonian dynamics, in which machine-learned surrogates accelerate N-body ensembles and enable Bayesian inference of migration scenarios from the expanding observational census. A sympathetic reader would care because, if correct, the Kuiper Belt becomes a decisive testbed for distinguishing smooth versus grainy Neptune migration, constraining the primordial disk, and potentially revealing unseen perturbers.

What carries the argument

The load-bearing mechanics are (1) mean-motion resonances with Neptune, described by a pendulum-like averaged Hamiltonian whose libration width and adiabatic capture probability control which objects get trapped and heated during migration; (2) secular resonances, i.e., commensurabilities between a body's perihelion/nodal precession and Neptune's eigenfrequencies, which shape the classical belt's edges and the 44-AU kernel; (3) the Chirikov resonance-overlap criterion and the associated diffusion coefficients D_a that quantify chaotic transport; and (4) the hierarchy of chaos indicators—Lyapunov exponents, the fast chaos detector MEGNO, SALI/GALI alignment indices, frequency map analysis, en

What would settle it

Find a TNO for which the standard short-time indicator suite flags strong chaos (short Lyapunov time, MEGNO/SALI chaos, fast entropy growth) but a direct multi-gigayear N-body integration keeps it confined near a resonance; that case would break the claimed transfer from indicators to long-term stability. Equivalently, a large, fully characterized survey could test the 44-AU kernel: if the debiased proper-element distribution of cold classical objects shows no narrow 44-AU excess, the primordial-kernel interpretation loses its observational anchor.

Watch

Extended reading notes

Core claim

On its own terms, the review's central claim is that Kuiper Belt architecture 'encodes the combined effects of primordial disk conditions and subsequent planetary migration.' Concretely, adiabatic resonance sweeping during Neptune's outward migration captured and heated objects into the 3:2, 2:1, and higher-order resonances while freezing in their eccentricities; secular resonances sculpted the classical-belt boundaries; and resonance overlap plus chaotic diffusion generated the transport pathways linking the belt to the Centaurs and Jupiter-family comets. The review further claims that modern chaos indicators—frequency diffusion, MEGNO, SALI/GALI, entropy growth, Lagrangian descriptors, and

Load-bearing premise

The classifications and transport rates built on short-time chaos indicators (Lyapunov exponents, MEGNO, SALI/GALI, entropy growth, recurrence divergence) are assumed to carry over to the gigayear stability of weakly chaotic trans-Neptunian orbits, even though the paper itself notes that sticky trajectories can outlive their Lyapunov times by huge factors.

Editorial extensions

If this is right

  • If the architecture truly encodes migration history, then measured resonance occupancies (e.g., the 3:2 and 2:1 populations and their libration amplitudes) directly constrain Neptune's migration speed, smoothness, and total distance traveled.
  • Validated chaos indicators make TNO classification automatable: as surveys deliver orders of magnitude more objects, short-integration indicator suites can flag resonant members, stable cold-classical objects, and scattering candidates without per-object gigayear integrations.
  • The anomalous-diffusion framework gives physical transport timescales connecting the Kuiper Belt to the Centaur and Jupiter-family comet reservoirs, predicting how quickly objects leak from resonances into planet-crossing orbits.
  • Hybrid machine-learning/physics surrogates would turn migration modeling into a tractable inverse problem, allowing thousands of N-body simulations to be replaced by fast surrogates that feed Bayesian inference against observed orbital distributions.
  • Proper-element-based debiasing (via frequency map analysis) is claimed to be essential; if adopted as standard practice, comparisons between synthetic and observed populations become systematically less biased.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the short-time-indicator-to-gigayear-stability transfer holds, the same indicator stack could be exported to exoplanet compact systems, asteroid-belt families, and Oort-cloud dynamics, giving observers a uniform 'stability map' from a single short integration.
  • A sharper test the review leaves implicit: train an ML surrogate on short integrations of the 34–50 AU region and ask whether it reproduces the 44-AU kernel and resonance occupancy; failure would be evidence for missing physics such as an unseen distant planet or a different migration path.
  • The admitted stickiness problem suggests an explicit benchmark: compare Lyapunov-based, entropy-based, and recurrence-based indicators head-to-head on sticky resonant trajectories and measure which best predicts actual escape time in gigayear integrations; the winner would become the preferred indicator for weakly chaotic TNOs.
  • Because the observed census is admitted to be a biased subset, the kernel's primordial interpretation is falsifiable by survey design: a deep, uniformly characterized survey that recovers the same 44-AU concentration in debiased proper-element space would strengthen it, while dilution would point to observational selection.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This review synthesizes the dynamics of trans-Neptunian objects, focusing on mean-motion and secular resonances, proper elements, chaotic diffusion, chaos indicators (Lyapunov exponents, MEGNO, SALI/GALI, frequency map analysis, entropy, Lagrangian descriptors, recurrence divergence), and machine-learning surrogates. The central thesis is that the present-day Kuiper Belt architecture—resonant populations, cold/hot classical dichotomy, the 44-AU kernel, and scattering/Centaur pathways—encodes the combined effects of primordial disk conditions and Neptune's migration, and that the most promising future direction is hybrid dynamical-statistical frameworks anchored in Hamiltonian dynamics.

Significance. The review is broad and mostly accurate in its textbook material: the resonance-width scaling, MEGNO/SALI definitions, and anomalous-diffusion power-law formalism are correctly stated and cited. Its value is pedagogical and synthetic, collecting recent methods (FAIR, entropy indicators, Lagrangian descriptors, recurrence divergence, ML classifiers) and placing them in a common framework. The manuscript explicitly acknowledges survey bias and ML robustness issues, which is a strength. However, because the quantitative transport synthesis relies on conflicting diffusion-coefficient estimates and on an unreviewed preprint of the authors' own, the review's numerical backbone is not currently reliable enough to support the stronger claims about encoding migration history.

major comments (3)
  1. [§2.1 vs §2.4, both citing [145]] Conflicting diffusion coefficients: §2.1 states D_a ~10^-4–10^-3 AU² Myr^-1 and says this moves bodies 'several tenths of an AU over Gyr'; §2.4 quotes D_a ~10^-6–10^-4 AU² Myr^-1 for the same coefficient, both citing [145]. At the lower end, sqrt(2D·1Gyr) ≈ 0.045 AU, not several tenths. Since these rates underpin the claimed resonance leakage, Centaur delivery, and the 'chaotic transport' component of the architecture-encoding argument, the 100× discrepancy is load-bearing. Reconcile by separating normal diffusion D from the anomalous D_α of [72], specifying the region and integration times, and verifying that [145] (a Jupiter-Trojan study) is applicable to TNOs.
  2. [§3.2.5 and Fig. 10] The 'recent study' on recurrence-plot divergence is supported by reference [31], which is the authors' own unpublished arXiv preprint (Daquin & Kovacs, 2026). The review then recommends recurrence-divergence as a method for TNO stability. This is circular support unless the preprint is explicitly identified as the authors' own work and its status (unrefereed) disclosed; ideally, validate against published methods or remove the claim from the review's recommended toolkit.
  3. [§1, §3.3, §3.2.4] The manuscript states that sticky trajectories can linger near resonance islands 'for times vastly exceeding their Lyapunov timescales' and that resonant objects show 'extended periods of quasi-stability punctuated by rapid transitions.' Yet §2.4 and §3.2.4 treat 2×10^5-yr diffusion maps [72] and short-time indicators (Lyapunov, MEGNO, SALI) as providing a quantitative framework for gigayear-scale stability. This is a load-bearing gap: add an explicit discussion of how short-time chaos indicators and D_α maps are extrapolated to Gyr timescales (e.g., as local escape-rate proxies rather than direct transport rates), or soften the quantitative claims about a 'fossilized' migration record.
minor comments (5)
  1. [§2.4, Fig. 4] Units of D_α are given as '(AU2/yr)2 yr^-α', which is dimensionally inconsistent with MSD = 2d D_α t^α. Use AU²/yr^α or define the exact dimensions in the text.
  2. [§2.4 vs §2.2] Resonance notation is inconsistent: '2:3 resonance' (in §2.4) and '1:2 MMR' (Fig. 2 caption) appear alongside '3:2' and '2:1' elsewhere. Adopt a single notation (e.g., particle:Neptune) and state it.
  3. [Figures] The figure captions refer to colored points and lines, but the figures themselves are not visible in the submitted text; ensure production includes them.
  4. [§2.2] The text refers to 'Equation (4)' before the equation is defined; reorder or use a forward reference.
  5. [References] Reference [30] is a preprint and [31] is an unreviewed preprint; mark their status in the bibliography or in the text for transparency.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the review's synthesis rests on external literature; the self-citations are methodological and not load-bearing for the central architecture-encoding claim.

full rationale

This is a review/synthesis, not an original derivation, and it contains no fitted parameter that is renamed as a prediction and no step that reduces an output to an input by construction. The central claim that Kuiper Belt architecture encodes primordial disk conditions and Neptune's migration is supported by a wide external literature (e.g., Malhotra 1995; Levison et al. 2008; Nesvorný 2015; Hahn & Malhotra 2005), not by the paper's own prior results. The paper also states its own evidentiary limits: it concedes that 'Sticky trajectories may linger near resonance islands for times vastly exceeding their Lyapunov timescales [110]' and that 'the observed population remains a biased subset of the true distribution' (Sec. 5). These admissions reduce any impression that short-time chaos indicators are being silently equated with gigayear stability. The derivation chain—averaged resonance Hamiltonians, adiabatic capture, resonance overlap, proper elements, stability indicators—uses standard definitions and does not define any target quantity in terms of itself. The only self-citations are methodological: the anomalous-diffusion maps of Kővári et al. (2023) used in Sec. 2.4 and the recurrence-divergence indicator of Daquin & Kovacs (2026) in Sec. 3.2.5/Fig. 10. These support specific tool recommendations, not the paper's central architecture-encoding claim, and are not statistical fits forced by the data. A separate quantitative concern, not a circularity, is that the quoted diffusion coefficients differ by two orders of magnitude between Secs. 2.1/2.3 (D_a ~ 10^-4 to 10^-3 AU^2/Myr) and Sec. 2.4 (D_a ~ 10^-6 to 10^-4 AU^2/Myr), both citing [145]; this internal inconsistency affects the transport synthesis but is a correctness risk, not a circular reduction. Overall, the paper's core content is independent of its few self-citations, so the circularity burden is minimal.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper contributes no fitted constants or new model entities; all numbers come from cited computations. The assumptions listed are the background physics and methodology the synthesis depends on.

assumptions (5)
  • domain assumption The restricted N-body gravitational model dominated by Neptune (via the averaged resonant Hamiltonian and secular Laplace-Lagrange theory) is an adequate representation of TNO dynamics.
    Sections 2.1-2.3 build resonance widths and secular forcing on this model; possible extra perturbers such as Planet Nine are discussed only as an open hypothesis in Section 5.
  • standard math The Chirikov resonance-overlap criterion and adiabatic capture theory are valid in the Kuiper Belt regime.
    Section 2.4 invokes the Chirikov criterion [17] and Section 2.1 uses adiabatic invariance to explain capture and transport; these are unproved background results in the paper.
  • domain assumption Short-time chaos indicators are reliable proxies for gigayear stability of weakly chaotic TNO orbits.
    Section 3 assumes indicator classifications correspond to long-term evolution, although Section 1's sticky-regime caveat undermines this link for some orbits.
  • domain assumption Observational surveys (CFEPS/OSSOS/DES) are sufficiently complete and bias-corrected for the claimed structural features.
    Used to define the kernel at 44 AU and resonance population ratios; Section 5 concedes that survey completeness and bias correction remain limitations.
  • ad hoc to paper Machine-learning surrogates generalize from short integrations to gigayear-scale predictions in TNO dynamics.
    Section 4 argues that ML models trained on 10^4-orbit simulations predict 10^9-orbit stability; transferring SPOCK and three-body results to TNOs is an extrapolation not demonstrated in this review.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Advanced Techniques in Stability Analysis of Trans-Neptunian Objects." pith.science (2026). https://pith.science/paper/Z65QYOJS

@misc{pith2026260713629,
  author       = {Pith},
  title        = {Pith review of: Advanced Techniques in Stability Analysis of Trans-Neptunian Objects},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z65QYOJS}},
  note         = {Machine review of arXiv:2607.13629}
}
read the original abstract

The trans-Neptunian region (30-50 AU) is a dynamically structured reservoir of icy planetesimals whose orbital architecture reflects resonant dynamics, chaotic transport, and long-term gravitational sculpting by the giant planets. This review synthesizes recent developments in the dynamical investigation of trans-Neptunian objects (TNOs), with an emphasis on mean-motion and secular resonances, as well as chaotic diffusion, in a system whose growing observational census makes it an ideal testbed for chaos detection methods. Classical indicators, including Lyapunov exponents, MEGNO, SALI/GALI, and frequency map analysis, provide the quantitative backbone for mapping TNO phase space and are complemented by modern approaches such as Lagrangian descriptors, the FAIR resonance identification method, entropy-based chaos indicators, and recurrence plot divergence methods. An anomalous diffusion framework, in which mean squared displacement scales as a power law in time, further enables classification of sub- and superdiffusive orbital transport. Machine learning has emerged as a powerful complement to traditional dynamical methods: surrogate classifiers, deep neural network solvers, and hybrid physics-data-driven frameworks together extend reliable prediction horizons in chaotic regimes and open new routes for Bayesian inference of migration scenarios. The review concludes that the most promising path forward lies in hybrid dynamical-statistical frameworks anchored to Hamiltonian dynamics, enabling efficient exploration of high-dimensional parameter spaces informed by the expanding body of trans-Neptunian observations.

Figures

Figures reproduced from arXiv: 2607.13629 by the authors.

Figure 1
Figure 1. Distribution of Kuiper Belt objects in the semimajor axis–eccentricity space, illustrating the dominant mean-motion resonances with Neptune [45]. Blue dots indicate long-term resonant objects, while pink dots show temporal libration of critical arguments. Gray dots represent the non-resonant TNOs. Green vertical lines are placed at the locations of major mean-motion commensurabilities, including the 3:2, 5:3, 7:4, 2… view at source ↗
Figure 2
Figure 2. The minimal resonance angle ϕmin (related to Equation (2)), an indicator of orbital stability, is color coded during the 34Myr integration time in the (a, e) plane. The 1:2 MMR is explored according to the locations of the secular resonances for various inclinations, i = 0, 20, 40 degs. For low inclinations (top and middle panels) the g = 2s and s8 proper frequencies act almost identically; that is, they are respons… view at source ↗
Figure 3
Figure 3. The ifree values for 10Myr integration as a function of the barycentric semimajor axis. Top panel: The resonant (yellow) and classical (light (ifree < 4 ◦ ) and dark blue ifree > 4 ◦ ) TNOs are marked. The ν8 and ν18 secular resonances are also depicted for two eccentricity values. Bottom panel: ifree range = max ifree − min ifree indicates that the method of double-averaged Hamiltonian preserves inclination con￾ser… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Depicting the extended diffusion coefficients Dα in the (a, e) plane ac￾cording to mean square displacemant MSD x(t) = 2dDαt α [72], where d is the dimen￾sionality of state space vector x, Dα is the generalized diffusion coefficient, and the diffusion exponent α determ…
Figure 5
Figure 5. Figure 5: Stability map of the TNO region based on the maximum eccentricity method. Non-resonant (white), short-term (pink), and long-term (blue) resonant real TNOs are marked to show the dynamical importance of mean-motion resonances. The Neptune- and Uranus-crossing orbits are…
Figure 6
Figure 6. Figure 6: Dynamical map of Poincar´e section (p, py) in the H´enon-Heiles system with the Lagrangian Descriptor indicator. LD represents the accurate texture of the dynamics, including invariant curves, chaotic bands, and sticky regions. Source of figure: [32]. 3.2.2. FAIR: Fast…
Figure 7
Figure 7. Figure 7: The asteroid 2007 TC434 captured in 9:1 MMR with Neptune [44]. The upper left panel shows the Λ − Λ ′ vs. M, the difference of mean longitudes and mean anomaly, respectively, plane used to determine the type, order, and degree of the resonance by applying the FAIR meth…
Figure 8
Figure 8. Figure 8: Phase space portrait of the 4D Hamiltonian resonance web (see Equa￾tion (1) in [48]) for parameters ϵ = 0.25, γ = 0.1, µ = 0.5. Contour plot for S (left) and S ′ ∼ dS/dt (right, in logarithmic scale) for a grid of 500 × 500 initial conditions after t = 5 × 105 . The fi…
Figure 9
Figure 9. Figure 9: Heat map of the stability times computed from the Shannon entropy based on x = (L, G, H) in the 34-40 AU region of the trans-Neptunian space (between the eccentricities 0 ≤ e ≤ 0.6). Here, L, G, H denote the Delaunay actions (of dimension AU2 yr−1 ). The (a, e) pairs d…
Figure 10
Figure 10. Figure 10: (Left) Phase portrait for the resonance overlap Hamiltonian [31] ob￾tained with its associated Poincar´e map. (Right) The ensemble averages of the chaos indicator DIV follow distinct power laws on the regular (blue) and chaotic (red) components. The initial conditions…
Figure 11
Figure 11. Figure 11: A cartoon of the SPOCK (Stability of Planetary Orbital Configurations Klassifier) workflow. The method involves supervised learning (XGBoost) based on a 10-dimensional feature parameter space. The training data is a set of short-term integration of closed three-planet…
Figure 12
Figure 12. Figure 12: Graph networks [GN] (nodes and edges) trained by real observational data of the Solar System objects (sun, planets, and moons). By optimizing the parameters of the GN neural network edge functions, it is possible to fit the force expression, which, in the planetary ca…
Figure 13
Figure 13. Figure 13: Upper 3 panels: Prediction of the Lorenz system [94] using the reservoir computing model with the extension of the knowledge-based predictor loop. The blue line shows the ground truth of a strongly chaotic system, and the red dashed line indicates the hybrid predictio…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

160 extracted references · 60 canonical work pages

  1. [145]

    Chaotic Diffusion And Effective Stability of Jupiter Trojans.Celestial Mechanics and Dynamical Astronomy, 92(1-3):71–87, April 2005

    Kleomenis Tsiganis, Harry Varvoglis, and Rudolf Dvorak. Chaotic Diffusion And Effective Stability of Jupiter Trojans.Celestial Mechanics and Dynamical Astronomy, 92(1-3):71–87, April 2005. doi: 10.1007/s10569-004-3975-7

    work page doi:10.1007/s10569-004-3975-7 2005

  2. [72]

    K˝ ov´ ari, E

    E. K˝ ov´ ari, E. Forg´ acs-Dajka, T. Kov´ acs, Cs Kiss, and Zs S´ andor. A dynamical survey of the trans-Neptunian region - II. On the nature of chaotic diffusion.Monthly Notices of the Royal Astronomical Society, 524(1):L26–L31, September 2023. doi: 10.1093/mnrasl/slad063

    work page doi:10.1093/mnrasl/slad063 2023

  3. [31]

    Leveraging temporal features of the divergence quantifier of recurrence plot to detect chaos in conservative systems, 2026

    Jerome Daquin and Tamas Kovacs. Leveraging temporal features of the divergence quantifier of recurrence plot to detect chaos in conservative systems, 2026. URLhttps://arxiv.org/abs/ 2510.19042

    arXiv 2026

  4. [1]

    Bannister, J

    Michele T. Bannister, J. J. Kavelaars, Jean-Marc Petit, Brett J. Gladman, Stephen D. J. Gwyn, Ying-Tung Chen, Kathryn Volk, Mike Alexandersen, Susan D. Benecchi, Audrey Delsanti, Wes- ley C. Fraser, Mikael Granvik, Will M. Grundy, Aur´ elie Guilbert-Lepoutre, Daniel Hestroffer, SMALL BODY DYNAMICS 27 Wing-Huen Ip, Marian Jakubik, R. Lynne Jones, Nathan Ka...

    2016

  5. [2]

    Bannister, Brett J

    Michele T. Bannister, Brett J. Gladman, J. J. Kavelaars, Jean-Marc Petit, Kathryn Volk, Ying- Tung Chen, Mike Alexandersen, Stephen D. J. Gwyn, Megan E. Schwamb, Edward Ashton, Susan D. Benecchi, Nahuel Cabral, Rebekah I. Dawson, Audrey Delsanti, Wesley C. Fraser, Mikael Granvik, Sarah Greenstreet, Aur´ elie Guilbert-Lepoutre, Wing-Huen Ip, Marian Jakubik...

    2018

  6. [3]

    Konstantin Batygin and Michael E. Brown. Generation of Highly Inclined Trans-Neptunian Objects by Planet Nine.The Astrophysical Journal Letters, 833(1):L3, December 2016. doi: 10.3847/2041-8205/833/1/L3

    doi:10.3847/2041-8205/833/1/l3 2016

  7. [4]

    Beaug´ e and F

    C. Beaug´ e and F. Roig. A Semianalytical Model for the Motion of the Trojan Asteroids: Proper Elements and Families.Icarus, 153(2):391–415, October 2001. doi: 10.1006/icar.2001.6699

    arXiv 2001

  8. [5]

    Benecchi and Scott S

    Susan D. Benecchi and Scott S. Sheppard. Light Curves of 32 Large Transneptunian Objects. Astronomical Journal, 145(5):124, May 2013. doi: 10.1088/0004-6256/145/5/124

    doi:10.1088/0004-6256/145/5/124 2013

Show all 160 references
  1. [6]

    Benettin, L

    G. Benettin, L. Galgani, A. Giorgilli, and J.-M. Strelcyn. Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems - A method for computing all of them. I - Theory. II - Numerical application.Meccanica, 15:9–30, March 1980. doi: 10.1007/BF02128236

    1980 doi

  2. [7]

    On the reliability of N-body simulations.Com- putational Astrophysics and Cosmology, 2:2, March 2015

    Tjarda Boekholt and Simon Portegies Zwart. On the reliability of N-body simulations.Com- putational Astrophysics and Cosmology, 2:2, March 2015. doi: 10.1186/s40668-014-0005-3

    2015 doi

  3. [9]

    Borderies and P

    N. Borderies and P. Goldreich. A Simple Derivation of Capture Probabilities for the J+1:J and J+2:J Orbit-Orbit Resonance Problems.Celestial Mechanics, 32(2):127–136, February 1984. doi: 10.1007/BF01231120

    1984 doi

  4. [10]

    Breen, Christopher N

    Philip G. Breen, Christopher N. Foley, Tjarda Boekholt, and Simon Portegies Zwart. Newton versus the machine: solving the chaotic three-body problem using deep neural networks.Monthly Notices of the Royal Astronomical Society, 494(2):2465–2470, May 2020. doi: 10.1093/mnras/ staa713

    2020 doi

  5. [11]

    Sebastian F. M. Breitenbach, Jess F. Adkins, Hanno Meyer, Norbert Marwan, Kanikicharla Kr- ishna Kumar, and Gerald H. Haug. Strong influence of water vapor source dynamics on stable isotopes in precipitation observed in Southern Meghalaya NE India.Earth and Planetary Science L...

    2010 doi

  6. [12]

    Brown, Kristina M

    Michael E. Brown, Kristina M. Barkume, Darin Ragozzine, and Emily L. Schaller. A collisional family of icy objects in the Kuiper belt.Nature, 446(7133):294–296, March 2007. doi: 10.1038/ nature05619

    2007

  7. [13]

    John R. Cary, D. F. Escande, and J. L. Tennyson. Adiabatic-invariant change due to separatrix crossing.Physical Review A, 34(5):4256–4275, November 1986. doi: 10.1103/PhysRevA.34.4256

    1986 doi

  8. [14]

    XGBoost: A Scalable Tree Boosting System.arXiv e-prints, art

    Tianqi Chen and Carlos Guestrin. XGBoost: A Scalable Tree Boosting System.arXiv e-prints, art. arXiv:1603.02754, March 2016. doi: 10.48550/arXiv.1603.02754. 28 T. KOV ´ACS

    2016 doi arXiv

  9. [15]

    E. I. Chiang and A. B. Jordan. On the Plutinos and Twotinos of the Kuiper Belt.Astronomical Journal, 124(6):3430–3444, December 2002. doi: 10.1086/344605

    2002 doi

  10. [16]

    E. I. Chiang, A. B. Jordan, R. L. Millis, M. W. Buie, L. H. Wasserman, J. L. Elliot, S. D. Kern, D. E. Trilling, K. J. Meech, and R. M. Wagner. Resonance Occupation in the Kuiper Belt: Case Examples of the 5:2 and Trojan Resonances.Astronomical Journal, 126(1):430–443, July 20...

    2003 doi

  11. [17]

    Chirikov

    Boris V. Chirikov. A universal instability of many-dimensional oscillator systems.Physics Reports, 52(5):263–379, May 1979. doi: 10.1016/0370-1573(79)90023-1

    1979 doi

  12. [18]

    P. M. Cincotta and C. Sim´ o. Simple tools to study global dynamics in non-axisymmetric galactic potentials - I.Astronomy and Astrophysics Supplement, 147:205–228, December 2000. doi: 10.1051/aas:2000108

    doi

  13. [19]

    P. M. Cincotta, C. M. Giordano, and C. Sim´ o. Phase space structure of multi-dimensional systems by means of the mean exponential growth factor of nearby orbits.Physica D Nonlinear Phenomena, 182(3-4):151–178, August 2003. doi: 10.1016/S0167-2789(03)00103-9

    2003 doi

  14. [20]

    P. M. Cincotta, C. M. Giordano, J. G. Mart ´ ı, and C. Beaug´ e. On the chaotic diffusion in multidimensional Hamiltonian systems.Celestial Mechanics and Dynamical Astronomy, 130(1): 7, January 2018. doi: 10.1007/s10569-017-9797-1

    2018 doi

  15. [21]

    Cincotta and Claudia M

    Pablo M. Cincotta and Claudia M. Giordano. Estimation of diffusion time with the Shannon entropy approach.Physical Review E, 107(6):064101, June 2023. doi: 10.1103/PhysRevE.107. 064101

    2023 doi

  16. [22]

    Cincotta, Christos Efthymiopoulos, Claudia M

    Pablo M. Cincotta, Christos Efthymiopoulos, Claudia M. Giordano, and Mart ´ ın F. Mestre. Chirikov and Nekhoroshev diffusion estimates: Bridging the two sides of the river.Physica D Nonlinear Phenomena, 266:49–64, January 2014. doi: 10.1016/j.physd.2013.10.005

    2014 doi

  17. [23]

    Cincotta, Claudia M

    Pablo M. Cincotta, Claudia M. Giordano, Raphael Alves Silva, and Cristi´ an Beaug´ e. The Shannon entropy: An efficient indicator of dynamical stability.Physica D Nonlinear Phenomena, 417:132816, March 2021. doi: 10.1016/j.physd.2020.132816

    2021

  18. [24]

    Cincotta, Claudia M

    Pablo M. Cincotta, Claudia M. Giordano, Raphael Alves Silva, and Cristi´ an Beaug´ e. Shannon entropy diffusion estimates: sensitivity on the parameters of the method.Celestial Mechanics and Dynamical Astronomy, 133(2):7, February 2021. doi: 10.1007/s10569-021-10006-y

    2021 doi

  19. [25]

    Cincotta, Claudia M

    Pablo M. Cincotta, Claudia M. Giordano, and Ivan I. Shevchenko. Revisiting the relation between the Lyapunov time and the instability time.Physica D Nonlinear Phenomena, 430: 133101, February 2022. doi: 10.1016/j.physd.2021.133101

    2022

  20. [26]

    Comp` ere, D

    A. Comp` ere, D. Farrelly, A. Lema ˆ ıtre, and D. Hestroffer. A possible mechanism to explain the lack of binary asteroids among the Plutinos.Astronomy and Astrophyics, 558:A4, October 2013. doi: 10.1051/0004-6361/201321137

    2013 doi

  21. [27]

    Cordeiro

    Ricardo R. Cordeiro. Anomalous Diffusion in the Asteroid Belt.Astronomical Journal, 132(5): 2114–2126, November 2006. doi: 10.1086/508193

    2006 doi

  22. [28]

    Solar System Formation.Reviews in Modern Astronomy, 21:215–227, January

    Aur´ elien Crida. Solar System Formation.Reviews in Modern Astronomy, 21:215–227, January

  23. [29]

    Improved detection of chaos with Lagrangian descriptors using differential algebra.Physica D Nonlinear Phenomena, 472:134506, February 2025

    Alexandru C˘ aliman, J´ erˆ ome Daquin, and Anne-Sophie Libert. Improved detection of chaos with Lagrangian descriptors using differential algebra.Physica D Nonlinear Phenomena, 472:134506, February 2025. doi: 10.1016/j.physd.2024.134506

    2025

  24. [30]

    Lagrangian descriptors and their applications to deterministic chaos.arXiv e-prints, art

    Jerome Daquin. Lagrangian descriptors and their applications to deterministic chaos.arXiv e-prints, art. arXiv:2309.10643, September 2023. doi: 10.48550/arXiv.2309.10643

    2023 doi arXiv

  25. [32]

    Global dynamics visualisation from Lagrangian Descriptors

    J´ erˆ ome Daquin, R´ emi P´ edenon-Orlanducci, Makrina Agaoglou, Guillermo Garc ´ ıa-S´ anchez, and Ana Maria Mancho. Global dynamics visualisation from Lagrangian Descriptors. Applications to discrete and continuous systems.Physica D Nonlinear Phenomena, 442:133520, December

  26. [33]

    Discovering the Surface Composition of TNOs (DiSCo-TNOs) with the James Webb Space Telescope

    Mario De Pra, Noemi Pinilla-Alonso, Ana Carolina Souza Feliciano, Charles Schambeau, Brit- tany Harvison, Josh Emery, Dale Cruikshank, Yvonne Pendleton, Bryan Holler, John Stans- berry, Vania Lorenzi, Thomas Muller, Aur´ elie Guilbert-Lepoutre, Nuno Peixinho, Michele Ban- nist...

    2022 doi

  27. [34]

    Deck, Matthew Payne, and Matthew J

    Katherine M. Deck, Matthew Payne, and Matthew J. Holman. First-order Resonance Overlap and the Stability of Close Two-planet Systems.The Astrophysical Journal, 774(2):129, Septem- ber 2013. doi: 10.1088/0004-637X/774/2/129

    2013 doi

  28. [35]

    S. J. Desch. Mass Distribution and Planet Formation in the Solar Nebula.The Astrophysical Journal, 671(1):878–893, December 2007. doi: 10.1086/522825

    2007 doi

  29. [36]

    Origin and Evolution of the Cometary Reservoirs.Space Science Reviews, 197(1-4):191–269, December 2015

    Luke Dones, Ramon Brasser, Nathan Kaib, and Hans Rickman. Origin and Evolution of the Cometary Reservoirs.Space Science Reviews, 197(1-4):191–269, December 2015. doi: 10.1007/ s11214-015-0223-2

    2015

  30. [37]

    M. J. Duncan and H. F. Levison. A scattered comet disk and the origin of Jupiter family comets. Science, 276:1670–1672, June 1997. doi: 10.1126/science.276.5319.1670

    1997

  31. [38]

    Duncan, Harold F

    Martin J. Duncan, Harold F. Levison, and Stuart Mark Budd. The Dynamical Structure of the Kuiper Belt.Astronomical Journal, 110:3073, December 1995. doi: 10.1086/117748

    1995 doi

  32. [39]

    On the Stability Regions of the Trojan Asteroids

    Rudolf Dvorak and Richard Schwarz. On the Stability Regions of the Trojan Asteroids. Celestial Mechanics and Dynamical Astronomy, 92(1-3):19–28, April 2005. doi: 10.1007/ s10569-005-2630-2

    2005

  33. [40]

    Eckmann, S

    J.-P. Eckmann, S. Oliffson Kamphorst, and D. Ruelle. Recurrence plots of dynamical systems. EPL (Europhysics Letters), 4:973, November 1987. doi: 10.1209/0295-5075/4/9/004

    1987 doi

  34. [41]

    J. L. Elliot, S. D. Kern, K. B. Clancy, A. A. S. Gulbis, R. L. Millis, M. W. Buie, L. H. Wasserman, E. I. Chiang, A. B. Jordan, D. E. Trilling, and K. J. Meech. The Deep Ecliptic Survey: A Search for Kuiper Belt Objects and Centaurs. II. Dynamical Classification the Kuiper Bel...

    2005 doi

  35. [42]

    V. V. Emel’yanenko. Features of the Dynamical Evolution of a Massive Disk of Trans-Neptunian Objects.Solar System Research, 55(4):341–347, July 2021. doi: 10.1134/S0038094621040055

    2021 doi

  36. [43]

    Forg´ acs-Dajka, Zs S´ andor, and B.´Erdi

    E. Forg´ acs-Dajka, Zs S´ andor, and B.´Erdi. A fast method to identify mean motion resonances. Monthly Notices of the Royal Astronomical Society, 477(3):3383–3389, July 2018. doi: 10.1093/ mnras/sty641

    2018

  37. [44]

    Forg´ acs-Dajka, Zs

    E. Forg´ acs-Dajka, Zs. S´ andor, and J. Sztakovics. A survey on Hungaria asteroids involved in mean motion resonances with Mars.Astronomy and Astrophysics, 657:A135, January 2022. doi: 10.1051/0004-6361/202141719

    2022 doi

  38. [45]

    Forg´ acs-Dajka, E

    E. Forg´ acs-Dajka, E. K˝ ov´ ari, T. Kov´ acs, Cs. Kiss, and Zs. S´ andor. A Dynamical Survey of the Trans-Neptunian Region. I. Mean-motion Resonances with Neptune.The Astrophysical Journal Supplement Series, 266(1):5, May 2023. doi: 10.3847/1538-4365/acc4c8

    2023 doi

  39. [46]

    Roman Frigg. In what sense is the kolmogorov-sinai entropy a measure for chaotic behaviour? bridging the gap between dynamical systems theory and communication theory.The British Journal for the Philosophy of Science, 55(3):411–434, 2004. ISSN 00070882, 14643537. URL http://ww...

    2004

  40. [47]

    Froeschl´ e, R

    Cl. Froeschl´ e, R. Gonczi, and E. Lega. The fast Lyapunov indicator: a simple tool to detect weak chaos. Application to the structure of the main asteroidal belt.Planetary and Space Science, 45(7):881–886, July 1997. doi: 10.1016/S0032-0633(97)00058-5

    1997 doi

  41. [48]

    C. M. Giordano and P. M. Cincotta. The Shannon entropy as a measure of diffusion in multidi- mensional dynamical systems.Celestial Mechanics and Dynamical Astronomy, 130(5):35, May

  42. [49]

    Gladman, B

    B. Gladman, B. G. Marsden, and C. Vanlaerhoven. Nomenclature in the Outer Solar System. In M. A. Barucci, H. Boehnhardt, D. P. Cruikshank, A. Morbidelli, and Renee Dotson, editors, 30 T. KOV ´ACS The Solar System Beyond Neptune, pages 43–57. 2008

    2008

  43. [50]

    Gladman, S

    B. Gladman, S. M. Lawler, J.-M. Petit, J. Kavelaars, R. L. Jones, J. Wm. Parker, C. Van Laerhoven, P. Nicholson, P. Rousselot, A. Bieryla, and M. L. N. Ashby. The Resonant Trans- Neptunian Populations.Astronomical Journal, 144(1):23, July 2012. doi: 10.1088/0004-6256/ 144/1/23

    2012 doi

  44. [51]

    On the Fates of Minor Bodies in the Outer Solar System

    Brett Gladman and Martin Duncan. On the Fates of Minor Bodies in the Outer Solar System. Astronomical Journal, 100:1680, November 1990. doi: 10.1086/115628

    1990 doi

  45. [52]

    Pawar, Vishnu R

    Vedasri Godavarthi, Samadhan A. Pawar, Vishnu R. Unni, R. I. Sujith, Norbert Marwan, and J¨ urgen Kurths. Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor.Chaos, 28(11):113111, November 2018. doi: 10.1063/1.5052210

    2018 doi

  46. [53]

    R. S. Gomes. Dynamical Effects of Planetary Migration on the Primordial Asteroid Belt.As- tronomical Journal, 114:396–401, July 1997. doi: 10.1086/118483

    1997 doi

  47. [54]

    R. S. Gomes, J. A. Fern´ andez, T. Gallardo, and A. Brunini. The Scattered Disk: Origins Dynamics and End States. In M. A. Barucci, H. Boehnhardt, D. P. Cruikshank, A. Morbidelli, and Renee Dotson, editors,The Solar System Beyond Neptune, pages 259–273. 2008

    2008

  48. [55]

    Rodney S. Gomes. The origin of the Kuiper Belt high-inclination population.Icarus, 161(2): 404–418, February 2003. doi: 10.1016/S0019-1035(02)00056-8

    2003 doi

  49. [56]

    Gomes, Alessandro Morbidelli, and Harold F

    Rodney S. Gomes, Alessandro Morbidelli, and Harold F. Levison. Planetary migration in a planetesimal disk: why did Neptune stop at 30 AU?Icarus, 170(2):492–507, August 2004. doi: 10.1016/j.icarus.2004.03.011

    2004 doi

  50. [57]

    Gomes, Tabar´ e Gallardo, Julio A

    Rodney S. Gomes, Tabar´ e Gallardo, Julio A. Fern´ andez, and Adri´ an Brunini. On The Origin of The High-Perihelion Scattered Disk: The Role of The Kozai Mechanism And Mean Motion Resonances.Celestial Mechanics and Dynamical Astronomy, 91(1-2):109–129, January 2005. doi: 10.1...

    2005 doi

  51. [58]

    Probing the Nekhoroshev Stability of Asteroids.Celestial Mechanics and Dynamical Astronomy, 83(1):121–140, May 2002

    Massimiliano Guzzo, Zoran Kneˇ zevi´ c, and Andrea Milani. Probing the Nekhoroshev Stability of Asteroids.Celestial Mechanics and Dynamical Astronomy, 83(1):121–140, May 2002. doi: 10.1023/A:1020182715182

    2002 doi

  52. [59]

    Hahn and Renu Malhotra

    Joseph M. Hahn and Renu Malhotra. Neptune’s Migration into a Stirred-Up Kuiper Belt: A Detailed Comparison of Simulations to Observations.Astronomical Journal, 130(5):2392–2414, November 2005. doi: 10.1086/452638

    2005 doi

  53. [60]

    J. Henrard. The adiabatic invariant - The use in celestial mechanics. In V. Szebehely, editor, Applications of Modern Dynamics to Celestial Mechanics and Astrodynamics, volume 82 of NATO Advanced Study Institute (ASI) Series C, pages 153–171, January 1982

    1982

  54. [61]

    J. Henrard. Capture Into Resonance - an Extension of the Use of Adiabatic Invariants.Celestial Mechanics, 27(1):3–22, May 1982. doi: 10.1007/BF01228946

    1982 doi

  55. [62]

    Henrard and A

    J. Henrard and A. Lemaitre. A Second Fundamental Model for Resonance.Celestial Mechanics, 30(2):197–218, June 1983. doi: 10.1007/BF01234306

    1983 doi

  56. [63]

    Capture probabilities for secondary resonances.Icarus, 95(2):244–252, February 1992

    Jacques Henrard and Michele Moons. Capture probabilities for secondary resonances.Icarus, 95(2):244–252, February 1992. doi: 10.1016/0019-1035(92)90041-5

    1992 doi

  57. [64]

    Reconstructing state spaces from multivariate data using variable delays.Physical Review E, 74(2):026202, August 2006

    Yoshito Hirata, Hideyuki Suzuki, and Kazuyuki Aihara. Reconstructing state spaces from multivariate data using variable delays.Physical Review E, 74(2):026202, August 2006. doi: 10.1103/PhysRevE.74.026202

    2006 doi

  58. [65]

    M. J. Holman and J. Wisdom. Dynamical Stability in the Outer Solar System and the Delivery of Short Period Comets.Astronomical Journal, 105:1987, May 1993. doi: 10.1086/116574

    1987 doi

  59. [66]

    Free Inclinations for Trans-Neptunian Ob- jects in the Main Kuiper Belt.The Astrophysical Journal Supplement Series, 259(2):54, April

    Yukun Huang, Brett Gladman, and Kathryn Volk. Free Inclinations for Trans-Neptunian Ob- jects in the Main Kuiper Belt.The Astrophysical Journal Supplement Series, 259(2):54, April

  60. [67]

    Shigeru Ida, Geoffrey Bryden, D. N. C. Lin, and Hidekazu Tanaka. Orbital Migration of Neptune and Orbital Distribution of Trans-Neptunian Objects.The Astrophysical Journal, 534(1):428– 445, May 2000. doi: 10.1086/308720. SMALL BODY DYNAMICS 31

    doi

  61. [68]

    Jewitt and J

    D. Jewitt and J. Luu. Discovery of the candidate Kuiper belt object 1992 QB 1.Nature, 362 (6422):730–732, April 1993. doi: 10.1038/362730a0

    1992 doi

  62. [69]

    R. L. Jones, B. Gladman, J.-M. Petit, P. Rousselot, O. Mousis, J. J. Kavelaars, A. Campo Bagatin, G. Bernabeu, P. Benavidez, J. Wm. Parker, P. Nicholson, M. Holman, T. Grav, A. Doressoundiram, C. Veillet, H. Scholl, and G. Mars. The CFEPS Kuiper Belt Survey: Strategy and presu...

    2006 doi

  63. [70]

    doi: 10.3847/1538-4365/ac559a

    doi

  64. [71]

    K˝ ov´ ari, B.´Erdi, and Zs S´ andor

    E. K˝ ov´ ari, B.´Erdi, and Zs S´ andor. Application of the Shannon entropy in the planar (non- restricted) four-body problem: the long-term stability of the Kepler-60 exoplanetary system. Monthly Notices of the Royal Astronomical Society, 509(1):884–893, January 2022. doi: 10...

    2022

  65. [73]

    Kingma and Jimmy Ba

    Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization. InInterna- tional Conference on Learning Representations (ICLR), 2015. URLhttps://arxiv.org/abs/ 1412.6980

    2015 arXiv

  66. [74]

    Khain, J

    T. Khain, J. C. Becker, and Hsing Wen et al. Lin. Dynamical Classification of Trans-Neptunian Objects Detected by the Dark Energy Survey.Astronomical Journal, 159(4):133, April 2020. doi: 10.3847/1538-3881/ab7002

    2020 doi

  67. [75]

    Secular resonance maps.Proceedings of the International Astronomical Union, 18(S382):130–135, 2022

    Zoran Kneˇ zevi´ c. Secular resonance maps.Proceedings of the International Astronomical Union, 18(S382):130–135, 2022. doi: 10.1017/S1743921323003885

    2022 doi

  68. [76]

    Recurrence plots and chaotic motion around Kerr black hole

    Ondˇ rej Kop´ aˇ cek, Jiˇ r ´ ı Kov´ aˇ r, Vladim ´ ır Karas, and Zdenˇ ek Stuchl ´ ık. Recurrence plots and chaotic motion around Kerr black hole. In Manuel de Le´ on, D. M. de Diego, and R. M. Ros, editors, Mathematics and Astronomy: A Joint Long Journey, volume 1283 ofAmeri...

    2010 doi

  69. [77]

    Kov´ acs

    T. Kov´ acs. Stability of exoplanetary systems retrieved from scalar time series.Monthly Notices of the Royal Astronomical Society, 491(3):3137–3154, January 2020. doi: 10.1093/mnras/stz3219

    2020 doi

  70. [78]

    Kneˇ zevi´ c and A

    Z. Kneˇ zevi´ c and A. Milani. Synthetic Proper Elements for Outer Main Belt Asteroids.Ce- lestial Mechanics and Dynamical Astronomy, 78:17–46, September 2000. doi: 10.1023/A: 1011187405509

    doi

  71. [79]

    Sanjukta Krishnagopal, Michelle Girvan, Edward Ott, and Brian R. Hunt. Separation of chaotic signals by reservoir computing.Chaos, 30(2):023123, February 2020. doi: 10.1063/1.5132766

    2020 doi

  72. [80]

    Neptune’s resonances in the scattered disk.Celestial Mechanics and Dynamical Astronomy, 131(8):39, August 2019

    Lei Lan and Renu Malhotra. Neptune’s resonances in the scattered disk.Celestial Mechanics and Dynamical Astronomy, 131(8):39, August 2019. doi: 10.1007/s10569-019-9917-1

    2019 doi

  73. [81]

    J. Laskar. The chaotic motion of the solar system: A numerical estimate of the size of the chaotic zones.Icarus, 88(2):266–291, December 1990. doi: 10.1016/0019-1035(90)90084-M

    1990 doi

  74. [82]

    Stability analysis of planetary systems via second-order R´ enyi entropy.Monthly Notices of the Royal Astronomical Society, 517(4):5160–5165, December 2022

    Tam´ as Kov´ acs, M´ at´ e Pszota, Emese K˝ ov´ ari, Emese Forg´ acs-Dajka, and Zsolt S´ andor. Stability analysis of planetary systems via second-order R´ enyi entropy.Monthly Notices of the Royal Astronomical Society, 517(4):5160–5165, December 2022. doi: 10.1093/mnras/stac3010

    2022 doi

  75. [83]

    Springer Netherlands, Dordrecht, 1999

    Jacques Laskar.Introduction to Frequency Map Analysis, pages 134–150. Springer Netherlands, Dordrecht, 1999. ISBN 978-94-011-4673-9. doi: 10.1007/978-94-011-4673-9 13. URLhttps: //doi.org/10.1007/978-94-011-4673-9_13

    1999 doi

  76. [84]

    S. M. Lawler, R. E. Pike, N. Kaib, M. Alexandersen, M. T. Bannister, Y.-T. Chen, B. Gladman, S. Gwyn, J. J. Kavelaars, J.-M. Petit, and K. Volk. OSSOS. XIII. Fossilized Resonant Dropouts Tentatively Confirm Neptune’s Migration Was Grainy and Slow.Astronomical Journal, 157(6): ...

    2019 doi

  77. [85]

    Franklin, Matthew J

    Myron Lecar, Fred A. Franklin, Matthew J. Holman, and Norman J. Murray. Chaos in the Solar System.Annual Review of Astronomy and Astropysics, 39:581–631, January 2001. doi: 32 T. KOV ´ACS 10.1146/annurev.astro.39.1.581

    2001 doi

  78. [86]

    Frequency Analysis of a Dynamical System.Celestial Mechanics and Dynamical Astronomy, 56(1-2):191–196, March 1993

    Jacques Laskar. Frequency Analysis of a Dynamical System.Celestial Mechanics and Dynamical Astronomy, 56(1-2):191–196, March 1993. doi: 10.1007/BF00699731

    1993 doi

  79. [87]

    Shannon entropy: a rigorous notion at the crossroads between probabil- ity information theory dynamical systems and statistical physics

    Annick Lesne. Shannon entropy: a rigorous notion at the crossroads between probabil- ity information theory dynamical systems and statistical physics. 24(3), 03 2014. doi: 10.1017/s0960129512000783. URLhttp://dx.doi.org/10.1017/s0960129512000783

    2014 doi

  80. [88]

    Levison and Alessandro Morbidelli

    Harold F. Levison and Alessandro Morbidelli. The formation of the Kuiper belt by the outward transport of bodies during Neptune’s migration.Nature, 426(6965):419–421, November 2003. doi: 10.1038/nature02120

    2003 doi

  81. [89]

    Levison, Alessandro Morbidelli, Christa Van Laerhoven, Rodney Gomes, and Kleome- nis Tsiganis

    Harold F. Levison, Alessandro Morbidelli, Christa Van Laerhoven, Rodney Gomes, and Kleome- nis Tsiganis. Origin of the structure of the Kuiper belt during a dynamical instability in the orbits of Uranus and Neptune.Icarus, 196(1):258–273, July 2008. doi: 10.1016/j.icarus.2007.11.035

    2008 doi

  82. [90]

    Rediscovering orbital mechanics with machine learning.Machine Learning: Science and Technology, 4(4): 045002, December 2023

    Pablo Lemos, Niall Jeffrey, Miles Cranmer, Shirley Ho, and Peter Battaglia. Rediscovering orbital mechanics with machine learning.Machine Learning: Science and Technology, 4(4): 045002, December 2023. doi: 10.1088/2632-2153/acfa63

    2023 doi

  83. [91]

    A study of the high-inclination population in the Kuiper belt - I

    Jian Li, Li-Yong Zhou, and Yi-Sui Sun. A study of the high-inclination population in the Kuiper belt - I. The Plutinos.Monthly Notices of the Royal Astronomical Society, 437(1): 215–226, January 2014. doi: 10.1093/mnras/stt1872

    2014 doi

  84. [92]

    Theory of Secular Chaos and Mercury’s Orbit.The Astro- physical Journal, 739(1):31, September 2011

    Yoram Lithwick and Yanqin Wu. Theory of Secular Chaos and Mercury’s Orbit.The Astro- physical Journal, 739(1):31, September 2011. doi: 10.1088/0004-637X/739/1/31

    2011 doi

  85. [93]

    Extracting Planet Mass and Eccentricity from TTV Data.The Astrophysical Journal, 761(2):122, December 2012

    Yoram Lithwick, Jiwei Xie, and Yanqin Wu. Extracting Planet Mass and Eccentricity from TTV Data.The Astrophysical Journal, 761(2):122, December 2012. doi: 10.1088/0004-637X/ 761/2/122

    2012 doi

  86. [94]

    Secular structure of 1:2 and 1:3 mean motion resonances with Neptune.Astnronomy and Astrophysics, 687:A206, July 2024

    Hailiang Li and Li-Yong Zhou. Secular structure of 1:2 and 1:3 mean motion resonances with Neptune.Astnronomy and Astrophysics, 687:A206, July 2024. doi: 10.1051/0004-6361/ 202449317

    2024 doi

  87. [95]

    Hunt, and Edward Ott

    Zhixin Lu, Brian R. Hunt, and Edward Ott. Attractor reconstruction by machine learning. Chaos, 28(6):061104, June 2018. doi: 10.1063/1.5039508

    2018 doi

  88. [96]

    P. S. Lykawka, J. Horner, B. W. Jones, and T. Mukai. Origin and dynamical evolution of Neptune Trojans - I. Formation and planetary migration.Monthly Notices of the Royal Astronomical Society, 398(4):1715–1729, October 2009. doi: 10.1111/j.1365-2966.2009.15243.x

    2009

  89. [97]

    P. S. Lykawka, J. Horner, B. W. Jones, and T. Mukai. Origin and dynamical evolution of Neptune Trojans - II. Long-term evolution.Monthly Notices of the Royal Astronomical Society, 412(1):537–550, March 2011. doi: 10.1111/j.1365-2966.2010.17936.x

    2011

  90. [98]

    Edward N. Lorenz. Deterministic Nonperiodic Flow.Journal of the Atmospheric Sciences, 20 (2):130–148, March 1963. doi: 10.1175/1520-0469(1963)020⟨0130:DNF⟩2.0.CO;2

    1963 doi

  91. [99]

    Exploring the 7:4 mean motion resonance—I: Dy- namical evolution of classical transneptunian objects.Planetary and Space Science, 53(11): 1175–1187, September 2005

    Patryk Sofia Lykawka and Tadashi Mukai. Exploring the 7:4 mean motion resonance—I: Dy- namical evolution of classical transneptunian objects.Planetary and Space Science, 53(11): 1175–1187, September 2005. doi: 10.1016/j.pss.2004.12.015

    2005 doi

  92. [100]

    Resonance sticking in the scattered disk.Icarus, 192 (1):238–247, December 2007

    Patryk Sofia Lykawka and Tadashi Mukai. Resonance sticking in the scattered disk.Icarus, 192 (1):238–247, December 2007. doi: 10.1016/j.icarus.2007.06.007

    2007 doi

  93. [101]

    Dynamical classification of trans-neptunian objects: Probing their origin evolution and interrelation.Icarus, 189(1):213–232, July 2007

    Patryk Sofia Lykawka and Tadashi Mukai. Dynamical classification of trans-neptunian objects: Probing their origin evolution and interrelation.Icarus, 189(1):213–232, July 2007. doi: 10. 1016/j.icarus.2007.01.001

    2007

  94. [102]

    Trans-Neptunian Objects as Natural Probes to the Unknown Solar System.Monographs on Environment, Earth and Planets, 1(3):121–186, December 2012

    Patryk Sofia Lykawka. Trans-Neptunian Objects as Natural Probes to the Unknown Solar System.Monographs on Environment, Earth and Planets, 1(3):121–186, December 2012. doi: 10.5047/meep.2012.00103.0121

    2012 arXiv

  95. [103]

    The Origin of Pluto’s Orbit: Implications for the Solar System Beyond Neptune

    Renu Malhotra. The Origin of Pluto’s Orbit: Implications for the Solar System Beyond Neptune. Astronomical Journal, 110:420, July 1995. doi: 10.1086/117532

    1995 doi

  96. [104]

    The Phase Space Structure Near Neptune Resonances in the Kuiper Belt

    Renu Malhotra. The Phase Space Structure Near Neptune Resonances in the Kuiper Belt. Astronomical Journal, 111:504, January 1996. doi: 10.1086/117802. SMALL BODY DYNAMICS 33

    1996 doi

  97. [105]

    Fraser, Rosemary E

    Micha¨ el Marsset, Wesley C. Fraser, Rosemary E. Pike, Michele T. Bannister, Megan E. Schwamb, Kathryn Volk, J. J. Kavelaars, Mike Alexandersen, Ying-Tung Chen, Brett J. Glad- man, Stephen D. J. Gwyn, Matthew J. Lehner, Nuno Peixinho, Jean-Marc Petit, and Shiang-Yu Wang. Col-O...

    2019 doi

  98. [106]

    Malhotra and S

    R. Malhotra and S. F. Dermott. The role of secondary resonances in the orbital history of Miranda.Icarus, 85(2):444–480, June 1990. doi: 10.1016/0019-1035(90)90126-T

    1990 doi

  99. [107]

    T. A. Michtchenko and S. Ferraz-Mello. Comparative study of the asteroidal motion in the 3:2 and 2:1 resonances with Jupiter. I. Planar model.Astronomy and Astrophysics, 303:945, November 1995

    1995

  100. [108]

    Secular perturbation theory and computation of asteroid proper elements.Celestial Mechanics and Dynamical Astronomy, 49(4):347–411, December 1990

    Andrea Milani and Zoran Knezevic. Secular perturbation theory and computation of asteroid proper elements.Celestial Mechanics and Dynamical Astronomy, 49(4):347–411, December 1990. doi: 10.1007/BF00049444

    1990 doi

  101. [109]

    Asteroid proper elements and secular resonances.Icarus, 98(2):211–232, August 1992

    Andrea Milani and Zoran Knezevic. Asteroid proper elements and secular resonances.Icarus, 98(2):211–232, August 1992. doi: 10.1016/0019-1035(92)90091-K

    1992 doi

  102. [110]

    Carmen Romano, Marco Thiel, and J¨ urgen Kurths

    Norbert Marwan, M. Carmen Romano, Marco Thiel, and J¨ urgen Kurths. Recurrence plots for the analysis of complex systems.Physics Reports, 438(5-6):237–329, January 2007. doi: 10.1016/j.physrep.2006.11.001

    2007 doi

  103. [111]

    Ambika, and Chandrakala Meena

    Athul Mohan, G. Ambika, and Chandrakala Meena. Deep learning for classifying dynamical states from time series via recurrence plots.arXiv e-prints, art. arXiv:2506.17498, June 2025. doi: 10.48550/arXiv.2506.17498

    2025 doi

  104. [112]

    Morbidelli, F

    A. Morbidelli, F. Thomas, and M. Moons. The Resonant Structure of the Kuiper Belt and the Dynamics of the First Five Trans-Neptunian Objects.Icarus, 118(2):322–340, December 1995. doi: 10.1006/icar.1995.1194

    1995

  105. [113]

    Morbidelli, H

    A. Morbidelli, H. F. Levison, and R. Gomes. The Dynamical Structure of the Kuiper Belt and Its Primordial Origin. In M. A. Barucci, H. Boehnhardt, D. P. Cruikshank, A. Morbidelli, and Renee Dotson, editors,The Solar System Beyond Neptune, pages 275–292. 2008. doi: 10.48550/arX...

    2008 doi arXiv

  106. [114]

    Andrea Milani and Anna M. Nobili. An example of stable chaos in the Solar System.Nature, 357(6379):569–571, June 1992. doi: 10.1038/357569a0

    1992 doi

  107. [115]

    Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location.Celestial Mechanics and Dynamical Astronomy, 51(2):131–167, June 1991

    Alessandro Morbidelli and Jacques Henrard. Secular resonances in the asteroid belt: Theoretical perturbation approach and the problem of their location.Celestial Mechanics and Dynamical Astronomy, 51(2):131–167, June 1991. doi: 10.1007/BF00048606

    1991 doi

  108. [116]

    Alessandro Morbidelli and Harold F. Levison. Kuiper Belt. Dynamics. In L. A. Adams Mc- Fadden, P. R. Weissman, and T. V. Johnson, editors,Encyclopedia of the Solar System, pages 589–604. 2007. doi: 10.1016/B978-012088589-3/50036-0

    2007 doi

  109. [117]

    Kuiper belt: formation and evolution

    Alessandro Morbidelli and David Nesvorn´ y. Kuiper belt: formation and evolution. In Dina Prialnik, Maria Antoinetta Barucci, and Leslie Young, editors,The Trans-Neptunian Solar System, pages 25–59. 2020. doi: 10.1016/B978-0-12-816490-7.00002-3

    2020 doi

  110. [118]

    Taylor & Francis, 2002

    Alessandro Morbidelli.Modern celestial mechanics : aspects of solar system dynamics. Taylor & Francis, 2002

    2002

  111. [119]

    Sweeping Secular Resonances in the Kuiper Belt Caused by Depletion of the Solar Nebula.Astronomical Journal, 120(6):3311–3322, December 2000

    Makiko Nagasawa and Shigeru Ida. Sweeping Secular Resonances in the Kuiper Belt Caused by Depletion of the Solar Nebula.Astronomical Journal, 120(6):3311–3322, December 2000. doi: 10.1086/316856

    doi

  112. [120]

    Nesvorn´ y and F

    D. Nesvorn´ y and F. Roig. Mean Motion Resonances in the Trans-neptunian Region. I. The 2:3 Resonance with Neptune.Icarus, 148(1):282–300, November 2000. doi: 10.1006/icar.2000.6480

  113. [121]

    Nesvorn´ y and F

    D. Nesvorn´ y and F. Roig. Mean Motion Resonances in the Transneptunian Region. Part II: The 1 : 2 3 : 4 and Weaker Resonances.Icarus, 150(1):104–123, March 2001. doi: 10.1006/icar. 2000.6568

    2001

  114. [122]

    Murray and Stanley F

    Carl D. Murray and Stanley F. Dermott.Solar System Dynamics. 1999. doi: 10.1017/ CBO9781139174817

    1999

  115. [123]

    Jumping Neptune Can Explain the Kuiper Belt Kernel.Astronomical Journal, 150(3):68, September 2015

    David Nesvorn´ y. Jumping Neptune Can Explain the Kuiper Belt Kernel.Astronomical Journal, 150(3):68, September 2015. doi: 10.1088/0004-6256/150/3/68

    2015 doi

  116. [124]

    Evidence for Slow Migration of Neptune from the Inclination Distri- bution of Kuiper Belt Objects.Astronomical Journal, 150(3):73, September 2015

    David Nesvorn´ y. Evidence for Slow Migration of Neptune from the Inclination Distri- bution of Kuiper Belt Objects.Astronomical Journal, 150(3):73, September 2015. doi: 10.1088/0004-6256/150/3/73

    2015 doi

  117. [125]

    Chaotic Capture of Neptune Trojans.Astronomical Journal, 137(6):5003–5011, June 2009

    David Nesvorn´ y and David Vokrouhlick´ y. Chaotic Capture of Neptune Trojans.Astronomical Journal, 137(6):5003–5011, June 2009. doi: 10.1088/0004-6256/137/6/5003

    2009 doi

  118. [126]

    Nesvorn´ y, F

    D. Nesvorn´ y, F. Roig, and S. Ferraz-Mello. Close Approaches of Trans-Neptunian Objects to Pluto Have Left Observable Signatures on Their Orbital Distribution.Astronomical Journal, 34 T. KOV ´ACS 119(2):953–969, February 2000. doi: 10.1086/301208

    doi

  119. [127]

    Edward Ott.Chaos in Dynamical Systems - 2nd Edition. 2002. doi: 10.2277/0521811961

    2002 doi

  120. [128]

    Hunt, Michelle Girvan, and Edward Ott

    Jaideep Pathak, Alexander Wikner, Rebeckah Fussell, Sarthak Chandra, Brian R. Hunt, Michelle Girvan, and Edward Ott. Hybrid forecasting of chaotic processes: Using machine learning in conjunction with a knowledge-based model.Chaos, 28(4):041101, April 2018. doi: 10.1063/1.5028373

    2018 doi

  121. [129]

    Petit, J

    J.-M. Petit, J. J. Kavelaars, B. J. Gladman, R. L. Jones, J. Wm. Parker, C. Van Laerhoven, P. Nicholson, G. Mars, P. Rousselot, O. Mousis, B. Marsden, A. Bieryla, M. Taylor, M. L. N. Ashby, P. Benavidez, A. Campo Bagatin, and G. Bernabeu. The Canada-France Ecliptic Plane Surve...

    2011 doi

  122. [130]

    Neptune’s Orbital Migration Was Grainy Not Smooth

    David Nesvorn´ y and David Vokrouhlick´ y. Neptune’s Orbital Migration Was Grainy Not Smooth. The Astrophysical Journal, 825(2):94, July 2016. doi: 10.3847/0004-637X/825/2/94

    2016 doi

  123. [131]

    Shevchenko

    Ivan I. Shevchenko. Hamiltonian intermittency and L´ evy flights in the three-body problem. Physical Review E, 81(6):066216, June 2010. doi: 10.1103/PhysRevE.81.066216

    2010 doi

  124. [132]

    Shevchenko.Dynamical Chaos in Planetary Systems, volume 463

    Ivan I. Shevchenko.Dynamical Chaos in Planetary Systems, volume 463. 2020. doi: 10.1007/ 978-3-030-52144-8

    2020

  125. [133]

    Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits.Journal of Physics A Mathematical General, 34(47):10029–10043, November

    Ch Skokos. Alignment indices: a new, simple method for determining the ordered or chaotic nature of orbits.Journal of Physics A Mathematical General, 34(47):10029–10043, November

  126. [134]

    Alice C. Quillen. Three-body resonance overlap in closely spaced multiple-planet systems. Monthly Notices of the Royal Astronomical Society, 418(2):1043–1054, December 2011. doi: 10.1111/j.1365-2966.2011.19555.x

    2011

  127. [135]

    Skokos, T

    Ch. Skokos, T. C. Bountis, and Ch. Antonopoulos. Geometrical properties of local dynamics in Hamiltonian systems: The Generalized Alignment Index (GALI) method.Physica D Nonlinear Phenomena, 231(1):30–54, July 2007. doi: 10.1016/j.physd.2007.04.004

    2007 doi

  128. [136]

    Michael Small and C. K. Tse. Optimal embedding parameters: a modelling paradigm.Physica D Nonlinear Phenomena, 194(3-4):283–296, July 2004. doi: 10.1016/j.physd.2004.03.006

    2004 doi

  129. [137]

    Detecting strange attractors in turbulence

    Floris Takens. Detecting strange attractors in turbulence. In David Rand and Lai-Sang Young, editors,Lecture Notes in Mathematics, Berlin Springer Verlag, volume 898, page 366. 1981. doi: 10.1007/BFb0091924

    1981 doi

  130. [138]

    Huang, Hanno Rein, Christa van Laerhoven, Adiv Paradise, Alysa Ober- tas, and Norman Murray

    Daniel Tamayo, Ari Silburt, Diana Valencia, Kristen Menou, Mohamad Ali-Dib, Cristobal Petro- vich, Chelsea X. Huang, Hanno Rein, Christa van Laerhoven, Adiv Paradise, Alysa Ober- tas, and Norman Murray. A Machine Learns to Predict the Stability of Tightly Packed Planetary Syst...

    2016 doi

  131. [139]

    Ch. Skokos. The Lyapunov Characteristic Exponents and Their Computation. In J. Souchay and R. Dvorak, editors,Lecture Notes in Physics, Berlin Springer Verlag, volume 790, pages 63–135. 2010. doi: 10.1007/978-3-642-04458-8 2

    2010 doi

  132. [140]

    J. L. Tennyson, J. R. Cary, and D. F. Escande. Change of the adiabatic invariant due to separa- trix crossing.Physical Review Letters, 56(20):2117–2120, May 1986. doi: 10.1103/PhysRevLett. 56.2117

    1986 doi

  133. [141]

    Tiscareno and Renu Malhotra

    Matthew S. Tiscareno and Renu Malhotra. Chaotic Diffusion of Resonant Kuiper Belt Objects. Astronomical Journal, 138(3):827–837, September 2009. doi: 10.1088/0004-6256/138/3/827

    2009 doi

  134. [142]

    Trujillo, David C

    Chadwick A. Trujillo, David C. Jewitt, and Jane X. Luu. Properties of the Trans-Neptunian Belt: Statistics from the Canada-France-Hawaii Telescope Survey.Astronomical Journal, 122 (1):457–473, July 2001. doi: 10.1086/321117

    2001 doi

  135. [143]

    Tsiganis, R

    K. Tsiganis, R. Gomes, A. Morbidelli, and H. F. Levison. Origin of the orbital architecture of the giant planets of the Solar System.Nature, 435(7041):459–461, May 2005. doi: 10.1038/ nature03539

    2005

  136. [144]

    Armitage, Shirley Ho, David N

    Daniel Tamayo, Miles Cranmer, Samuel Hadden, Hanno Rein, Peter Battaglia, Alysa Obertas, Philip J. Armitage, Shirley Ho, David N. Spergel, Christian Gilbertson, Naireen Hussain, Ari Silburt, Daniel Jontof-Hutter, and Kristen Menou. Predicting the long-term stability of compact...

    2020 doi

  137. [146]

    TNOs are Cool

    E. Vilenius, J. Stansberry, T. M¨ uller, M. Mueller, C. Kiss, P. Santos-Sanz, M. Mommert, A. P´ al, E. Lellouch, J. L. Ortiz, N. Peixinho, A. Thirouin, P. S. Lykawka, J. Horner, R. Duffard, S. Fornasier, and A. Delsanti. “TNOs are Cool”: A survey of the trans-Neptunian region....

    2018 doi

  138. [147]

    The Scattered Disk as the Source of the Jupiter Family Comets.The Astrophysical Journal, 687(1):714–725, November 2008

    Kathryn Volk and Renu Malhotra. The Scattered Disk as the Source of the Jupiter Family Comets.The Astrophysical Journal, 687(1):714–725, November 2008. doi: 10.1086/591839

    2008 doi

  139. [148]

    Inclination Mixing in the Classical Kuiper Belt.Tha Astro- physical Journal, 736(1):11, July 2011

    Kathryn Volk and Renu Malhotra. Inclination Mixing in the Classical Kuiper Belt.Tha Astro- physical Journal, 736(1):11, July 2011. doi: 10.1088/0004-637X/736/1/11

    2011 doi

  140. [149]

    Chaotic Diffusion of Asteroids

    Kleomenis Tsiganis. Chaotic Diffusion of Asteroids. In Daniel Benest, Claude Froeschle, and Elena Lega, editors,Lecture Notes in Physics, Berlin Springer Verlag, volume 729, page 111

  141. [150]

    The Evolution of Long-Period Comets.Icarus, 137(1):84–121, January 1999

    Paul Wiegert and Scott Tremaine. The Evolution of Long-Period Comets.Icarus, 137(1):84–121, January 1999. doi: 10.1006/icar.1998.6040

    1999

  142. [151]

    J. Wisdom. The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem.Astronomical Journal, 85:1122–1133, August 1980. doi: 10.1086/112778

    1980 doi

  143. [152]

    J. Wisdom. The origin of the Kirkwood gaps - A mapping for asteroidal motion near the 3/1 commensurability.Astronomical Journal, 87:577–593, March 1982. doi: 10.1086/113132

    1982 doi

  144. [153]

    J. Wisdom. A perturbative treatment of motion near the 3/1 commensurability.Icarus, 63(2): 272–289, August 1985. doi: 10.1016/0019-1035(85)90011-9

    1985 doi

  145. [154]

    Wisdom, S

    J. Wisdom, S. J. Peale, and F. Mignard. The chaotic rotation of Hyperion.Icarus, 58(2): 137–152, May 1984. doi: 10.1016/0019-1035(84)90032-0

    1984 doi

  146. [155]

    C. L. Webber, Jr. and J. P. Zbilut. Dynamical assessment of physiological systems and states using recurrence plot strategies.Journal of Applied Physiology, 76(2):965–973, February 1994. doi: 10.1152/jappl.1994.76.2.965

    1994 doi

  147. [161]

    Zbilut and Charles L

    Joseph P. Zbilut and Charles L. Webber. Embeddings and delays as derived from quan- tification of recurrence plots.Physics Letters A, 171(3-4):199–203, December 1992. doi: 10.1016/0375-9601(92)90426-M. Institute of Physics and Astronomy, E¨otv¨os University, Budapest, Hungary ...

    1992 doi

  148. [2001]

    doi: 10.1088/0305-4470/34/47/309

    doi

  149. [2007]

    doi: 10.1007/978-3-540-72984-6 5

    doi

  150. [2009]

    doi: 10.1002/9783527629190.ch11

    doi

  151. [2018]

    doi: 10.1007/s10569-018-9832-x

    doi

  152. [2022]

    SMALL BODY DYNAMICS 29

    doi: 10.1016/j.physd.2022.133520. SMALL BODY DYNAMICS 29

    2022

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.