Conditions for the Existence of SBR Measures for “Almost Anosov” Diffeomorphisms

DOI10.1090/S0002-9947-99-02477-0zbMath0949.37007OpenAlexW1648586922MaRDI QIDQ4942884

Huyi Hu

Publication date: 15 March 2000

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02477-0

zbMATH Keywords

invariant measureDirac measurealmost Anosov diffeomorphismSinai-Bowen-Ruelle measure

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20)

Related Items (21)

Infimum of the metric entropy of volume preserving Anosov systems ⋮ SRB measures of singular hyperbolic attractors ⋮ Pressure function and limit theorems for almost Anosov flows ⋮ Kupka–Smale diffeomorphisms at the boundary of uniform hyperbolicity: a model ⋮ (Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms ⋮ On volume preserving almost Anosov flows ⋮ Mixing rates of the geometrical neutral Lorenz model ⋮ The ergodicity of a class of almost Anosov systems ⋮ SRB measures for pointwise hyperbolic systems on open regions ⋮ SRB measures for almost Axiom A diffeomorphisms ⋮ Polynomial decay of correlations for almost Anosov diffeomorphisms ⋮ Some statistical properties of almost Anosov diffeomorphisms ⋮ Anatole Katok ⋮ Non-uniformly expanding dynamical systems: multi-dimension ⋮ Equilibrium states of almost Anosov diffeomorphisms ⋮ On Sinaĭ billiards on flat surfaces with horns ⋮ Regular variation and rates of mixing for infinite measure preserving almost Anosov diffeomorphisms ⋮ Almost sure rates of mixing for partially hyperbolic attractors ⋮ Mixing rates for symplectic almost Anosov maps ⋮ Mixing for invertible dynamical systems with infinite measure ⋮ Seminormal forms and cyclotomic quiver Hecke algebras of type \(A\).

Cites Work

• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• Sinai-Bowen-Ruelle measures for certain Hénon maps
• Propriétés ergodiques des mesures de Sinaï
• Sinai–Ruelle–Bowen measures for N-dimensional derived from Anosov diffeomorphisms
• A proof of the estimation from below in Pesin's entropy formula
• Dynamical systems with generalized hyperbolic attractors: hyperbolic, ergodic and topological properties
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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