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pith:JYZ7ML5A

pith:2026:JYZ7ML5A3STZQ53EZMK2A6MGVH

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Regularity of Lyapunov exponents at one-point Lyapunov spectra: the semisimple case

Marcelo Viana, Yingjian Liu

Lyapunov exponents are pointwise log-Hölder continuous with respect to the Wasserstein distance at semisimple probability measures with one-point Lyapunov spectrum.

arxiv:2605.16718 v1 · 2026-05-16 · math.DS · math.PR

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Claims

C1strongest claim

We prove that the Lyapunov exponents are pointwise log-Hölder continuous with respect to the Wasserstein distance, at semisimple probability measures with one-point Lyapunov spectrum.

C2weakest assumption

The probability measures under consideration admit a decomposition of the linear action into virtually conformal subspaces for which a Berry-Esseen type estimate holds for the associated random walk (as invoked in the proof strategy described in the abstract).

C3one line summary

Lyapunov exponents are pointwise log-Hölder continuous w.r.t. Wasserstein distance at semisimple measures with one-point spectrum.

References

300 extracted · 300 resolved · 0 Pith anchors

[1] Aaronson , TITLE = 1997

[2] F. Abdenur and L. J. D\' az. Shadowing in the C^1 topology

[3] F. Abdenur and A. Avila and J. Bochi , TITLE =. Proc. Amer. Math. Soc. , VOLUME =. 2004 , PAGES = 2004

[4] F. Abdenur. Generic robustness of spectral decompositions. Annales Scient. E.N.S. 2003 2003

[5] F. Abdenur. Attractors of generic diffeomorphisms are persistent. Nonlinearity

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:02:38.205310Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4e33f62fa0dca7987764cb15a07986a9f56ce736a74df185fed0fef7b7b870d5

Aliases

arxiv: 2605.16718 · arxiv_version: 2605.16718v1 · doi: 10.48550/arxiv.2605.16718 · pith_short_12: JYZ7ML5A3STZ · pith_short_16: JYZ7ML5A3STZQ53E · pith_short_8: JYZ7ML5A

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JYZ7ML5A3STZQ53EZMK2A6MGVH \
  | 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: 4e33f62fa0dca7987764cb15a07986a9f56ce736a74df185fed0fef7b7b870d5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5e53115a4fc5d1c3f2f98c29cd2100964d1a89fbf6fc832d775a56315ca95283",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-05-16T00:06:21Z",
    "title_canon_sha256": "e83fe0dbf9da5c1f25c690579269554dd81b8e6b2a05ecbabe80484ef34459a1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16718",
    "kind": "arxiv",
    "version": 1
  }
}