Pith Number

pith:WLZO3POS

pith:2026:WLZO3POSQB5JJKHUB3EZHFHEMJ

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Transfer Operators and SRB Measures for Axiom A Diffeomorphisms: Spectral Gap, Structural Stability, and the Gibbs Equivalence Theorem

Abdoulaye Thiam

The Gibbs Equivalence Theorem for SRB measures on mixing basic sets of Axiom A diffeomorphisms follows from structural stability, transfer-operator spectral gaps, and the Pesin entropy formula.

arxiv:2604.18929 v3 · 2026-04-21 · math.DS · math-ph · math.MP · math.PR

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Claims

C1strongest claim

The Gibbs Equivalence Theorem, assembling the symbolic, variational, spectral, and geometric characterizations of the equilibrium state on a mixing basic set, follows from these four Main Theorems together with the imported results of Parts I and III [64,66].

C2weakest assumption

The results depend on the Markov partition coding from Part III [66] to transfer symbolic spectral results from Part I [64] to smooth dynamics, plus the strong transversality condition for the structural stability theorem.

C3one line summary

Proves structural stability with explicit Hölder exponent, transfer operator quasi-compactness with spectral gap, SRB measures as unique equilibrium states with explicit unstable densities, and Pesin entropy formula for Axiom A diffeomorphisms, yielding the Gibbs Equivalence Theorem.

Cited by

6 papers in Pith

Statistical Limit Theorems for Axiom A Diffeomorphisms: Exponential Mixing, Central Limit Theorem, and Large Deviations

Multifractal Analysis, Liv\v{s}ic Rigidity, and Fluctuation Theorems for Axiom A Diffeomorphisms: The Pesin Formula and the Gallavotti-Cohen Symmetry

Statistical Limit Theorems for Axiom A Diffeomorphisms: Exponential Mixing, Central Limit Theorem, and Large Deviations

Uniform Hyperbolicity and Symbolic Dynamics: Markov Partitions, Shadowing, and the Coding of Axiom A Diffeomorphisms

Gibbs Measures on Subshifts of Finite Type: Five Equivalent Characterizations with Explicit Constants

Receipt and verification

First computed	2026-05-20T00:05:45.015561Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2f2edbdd2807a94a8f40ec99394e462504a1a8e684074043192a0467137e3af

Aliases

arxiv: 2604.18929 · arxiv_version: 2604.18929v3 · doi: 10.48550/arxiv.2604.18929 · pith_short_12: WLZO3POSQB5J · pith_short_16: WLZO3POSQB5JJKHU · pith_short_8: WLZO3POS

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WLZO3POSQB5JJKHUB3EZHFHEMJ \
  | 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: b2f2edbdd2807a94a8f40ec99394e462504a1a8e684074043192a0467137e3af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3dfa76665155f8b3c594f570172a8c2f398d22137181715c50dd9bbca6bdcd4b",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2026-04-21T00:08:49Z",
    "title_canon_sha256": "4329161bc9d009ac815bbb79e4f58cddfc7eac334a491973f64a8bbe95585ffe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18929",
    "kind": "arxiv",
    "version": 3
  }
}