Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’

DOI10.1017/S0143385700008245zbMath0818.58035MaRDI QIDQ4324893

Huyi Hu, Lai-Sang Young

Publication date: 8 August 1995

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

invariant measurealmost Anosov diffeomorphisms

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory (37A99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (38)

Infimum of the metric entropy of volume preserving Anosov systems ⋮ Dirac physical measures on saddle-type fixed points ⋮ Pressure function and limit theorems for almost Anosov flows ⋮ On $C^0$-centralizers of Anosov diffeomorphisms on the torus: algebraic and topological aspects ⋮ On the mathematical transport theory in microporous media: the billiard approach ⋮ (Semi)continuity of the entropy of Sinai probability measures for partially hyperbolic diffeomorphisms ⋮ Summable orbits ⋮ Weyl-flow and the conformally symplectic structure of thermostatted billiards: the problem of the hyperbolicity ⋮ Persistent non-statistical dynamics in one-dimensional maps ⋮ On Dirac physical measures for transitive flows ⋮ Mixing rates of the geometrical neutral Lorenz model ⋮ The ergodicity of a class of almost Anosov systems ⋮ Cherry flow: physical measures and perturbation theory ⋮ SRB measures for pointwise hyperbolic systems on open regions ⋮ Existence of SRB measures for hyperbolic maps with weak regularity ⋮ Poisson limit distribution for diffeomorphisms with weak hyperbolic product structure ⋮ Uniqueness of SRB measures for transitive diffeomorphisms on surfaces ⋮ SRB measures for almost Axiom A diffeomorphisms ⋮ Polynomial decay of correlations for almost Anosov diffeomorphisms ⋮ Some statistical properties of almost Anosov diffeomorphisms ⋮ Parameter-shifted shadowing property of Lozi maps ⋮ Anatole Katok ⋮ A note about Milnor attractor and riddled basin ⋮ Ergodic measures of SRB attractors ⋮ Non-uniformly expanding dynamical systems: multi-dimension ⋮ The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows ⋮ Dirac physical measures for generic diffeomorphisms ⋮ On Ilyashenko’s statistical attractors ⋮ Hyperbolic SRB measures and the leaf condition ⋮ Conditions for the Existence of SBR Measures for “Almost Anosov” Diffeomorphisms ⋮ Equilibrium states of almost Anosov diffeomorphisms ⋮ On the ergodicity of hyperbolic Sinaĭ–Ruelle–Bowen measures II: the low-dimensional case ⋮ Regular variation and rates of mixing for infinite measure preserving almost Anosov diffeomorphisms ⋮ \( \sigma \)-finite invariant densities for eventually conservative Markov operators ⋮ Mixing rates for symplectic almost Anosov maps ⋮ Recurrence times and rates of mixing ⋮ Mixing for invertible dynamical systems with infinite measure ⋮ Diffeomorphisms approximated by Anosov on the 2-torus and their SBR measures

Cites Work

• The dynamics of the Hénon map
• The metric entropy of diffeomorphisms. I: Characterization of measures satisfying Pesin's entropy formula
• First return map and invariant measures
• Propriétés ergodiques des mesures de Sinaï
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• LECTURES ON THE ENTROPY THEORY OF MEASURE-PRESERVING TRANSFORMATIONS

This page was built for publication: Nonexistence of SBR measures for some diffeomorphisms that are ‘Almost Anosov’