Pith. sign in

REVIEW 4 cited by

Invariance principle and non-compact center foliations

Not yet reviewed by Pith; the record is open.

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

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2210.14989 v2 pith:GLXJ2V7R submitted 2022-10-26 math.DS

Sylvain Crovisier , Mauricio Poletti This is my paper · ORCID
classification math.DS
keywords centeranosovflowsinvarianceinvariantmeasuremeasuresprinciple
verification ladder T0 review T1 audit T2 compute T3 formal

Signed reviews

No signed human review yet.

0 comments
read the original abstract

We prove a generalization of a so called "invariance principle" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center disintegration that is invariant by stable and unstable holonomies. This was known for systems admitting a foliation by compact center leaves, and we extend it to a larger class which contains discretized Anosov flows. We use our result to classify measures of maximal entropy and study physical measures for perturbations of the time-one map of Anosov flows.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

    math.DS 2025-05 conditional novelty 8.0 of 10

    Conservative partially hyperbolic diffeomorphisms homotopic to the identity on closed 3-manifolds with non-virtually-solvable fundamental group are always accessible and hence ergodic.

  2. Partially Hyperbolic Dynamics with Quasi-isometric Center

    math.DS 2024-11 conditional novelty 7.0 of 10

    Non-wandering partially hyperbolic diffeomorphisms with quasi-isometric center on closed 3-manifolds are either skew products over a torus Anosov map or discretized Anosov flows, and volume-preserving ones are ergodic.

  3. Quasi-isometric center action in dimension 3

    math.DS 2024-11 conditional novelty 7.0 of 10

    Transitive partially hyperbolic diffeomorphisms in dimension 3 that act quasi-isometrically on an invariant center foliation are classified up to finite lift and iterate as skew-products or discretised Anosov flows.

  4. Margulis Measures on Expanding Foliations: Construction and Rigidity

    math.DS 2026-07 conditional novelty 6.0 of 10

    Under homogeneous exponential growth, every measure maximizing entropy along an expanding one-dimensional foliation has conditional measures equivalent to a canonically constructed weak Margulis measure.

Pith tools