On physical measures of multi-singular hyperbolic vector fields

Xiaodong Wang, Sylvain Crovisier, Jinhua Zhang, Da-Wei Yang

Publication date: 8 January 2025

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Thermodynamic formalism, variational principles, equilibrium states for dynamical systems (37D35) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Cites Work

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On Pesin's entropy formula for dominated splittings without mixed behavior
Homoclinic classes for sectional-hyperbolic sets
On the singular-hyperbolicity of star flows
Diffeomorphisms with positive metric entropy
Existence and uniqueness of SRB measure on $C^1$ generic hyperbolic attractors
Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions
The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
A proof of the $C^ 1$ stability conjecture
Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
The ergodic theory of axiom A flows
Entropy on sphere bundles
A uniform $C^1$ connecting lemma.
Homoclinic tangencies and hyperbolicity for surface diffeomorphisms
A generalized shadowing lemma
Lyapunov stability of $\omega$-limit sets
Robust transitive singular sets for 3-flows are partially hyperbolic attractors or repellers
An ergodic closing lemma
Empirical measures of partially hyperbolic attractors
Entropy theory for sectional hyperbolic flows
Robust transitivity of singular hyperbolic attractors
Star flows and multisingular hyperbolicity
A countable partition for singular flows, and its application on the entropy theory
Entropy of physical measures for $C^\infty$ dynamical systems
On the notions of singular domination and (multi-)singular hyperbolicity
On the finiteness of uniform sinks
Propriétés ergodiques des mesures de Sinaï
Nonsingular star flows satisfy Axiom A and the no-cycle condition
Robustly transitive singular sets via approach of an extended linear Poincaré flow
Differentiable dynamical systems. An introduction to structural stability and hyperbolicity
Nonuniform hyperbolicity, global dominated splittings and generic properties of volume-preserving diffeomorphisms
Singular-hyperbolic attractors are chaotic
Nonuniform center bunching and the genericity of ergodicity among $C^1$ partially hyperbolic symplectomorphisms
An inequality for the entropy of differentiable maps
Regular Points for Ergodic Sinai Measures
Diffeomorphisms in ℱ¹(M) satisfy Axiom A
A Measure Associated with Axiom-A Attractors
𝐶¹ Connecting Lemmas
SRB measures for higher dimensional singular partially hyperbolic attractors
Deterministic Nonperiodic Flow
Morse-Smale systems and horseshoes for three dimensional singular flows
Finitely many physical measures for sectional-hyperbolic attracting sets and statistical stability
A new criterion of physical measures for partially hyperbolic diffeomorphisms
The Pesin entropy formula for diffeomorphisms with dominated splitting
GIBBS MEASURES IN ERGODIC THEORY
Analytic Quasi-Periodic Curves of Discontinuous Type on a Torus
Recurrence and genericity
Equilibrium states and the ergodic theory of Anosov diffeomorphisms
Invariant manifolds
A generic $C^1$ expanding map has a singular S-R-B measure
An entropy dichotomy for singular star flows
On the Existence of SRB Measures for ∞ Surface Diffeomorphisms
SRB measures for $C^{\infty}$ surface diffeomorphisms
A closing lemma for non-uniformly hyperbolic singular flows

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