Pith Number

pith:NGZU3VBY

pith:2026:NGZU3VBY6O7OHFUDHQQTWMG3Z2

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Robustly transitive behavior in symplectic dynamics

Jaime Paradela

Under a domination condition, real-analytic deformations of the product of a symplectomorphism with a basic set and one with a non-degenerate elliptic equilibrium produce large robustly transitive sets.

arxiv:2605.15922 v1 · 2026-05-15 · math.DS

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4 Citations open

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Claims

C1strongest claim

Under a domination condition we show that a broad class of real-analytic deformations of this system display large robustly transitive sets. As a corollary we also obtain new examples of real-analytic robustly transitive symplectomorphisms which are not uniformly hyperbolic.

C2weakest assumption

The domination condition between the basic set of the first symplectomorphism and the non-degenerate elliptic equilibrium of the second, which is invoked to guarantee that the blender horseshoes created by perturbation have a sufficiently large domain of influence.

C3one line summary

Under a domination condition, real-analytic deformations of symplectomorphism products yield large robustly transitive sets and new non-uniformly-hyperbolic examples via blender-horseshoe perturbations and control-theory ideas.

References

110 extracted · 110 resolved · 0 Pith anchors

[1] Partially hyperbolic dynamics in the 3-body problem , author=. 2025 , eprint= 2025

[2] Clarke, A. and Turaev, D. , TITLE =. Duke Math. J. , FJOURNAL =. 2023 , NUMBER =. doi:10.1215/00127094-2022-0073 , URL = 2023 · doi:10.1215/00127094-2022-0073

[3] Fayad, B. , TITLE =. J. Amer. Math. Soc. , FJOURNAL =. 2023 , NUMBER =. doi:10.1090/jams/997 , URL = 2023 · doi:10.1090/jams/997

[4] Bernard, P. and Kaloshin, V. and Zhang, K. , TITLE =. Acta Math. , FJOURNAL =. 2016 , NUMBER =. doi:10.1007/s11511-016-0141-5 , URL = 2016 · doi:10.1007/s11511-016-0141-5

[5] Kaloshin, V. and Zhang, K. , TITLE =. 2020 , PAGES = 2020

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:01:45.264124Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

69b34dd438f3bee396833c213b30dbceb0320fb5a1af5e8534616ddce34a61a4

Aliases

arxiv: 2605.15922 · arxiv_version: 2605.15922v1 · doi: 10.48550/arxiv.2605.15922 · pith_short_12: NGZU3VBY6O7O · pith_short_16: NGZU3VBY6O7OHFUD · pith_short_8: NGZU3VBY

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NGZU3VBY6O7OHFUDHQQTWMG3Z2 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 69b34dd438f3bee396833c213b30dbceb0320fb5a1af5e8534616ddce34a61a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "616cd72430f3379524309fff738e82f5246be457af2b66a4244709bb9d145afc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-15T13:05:11Z",
    "title_canon_sha256": "11b9c0e808a3d66904a0ba4161d58f51d7536faa276d474f950688423ca01475"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15922",
    "kind": "arxiv",
    "version": 1
  }
}