Diffeomorphisms satisfying the specification property

DOI10.1090/S0002-9939-09-10085-0zbMath1186.37012MaRDI QIDQ3402184

Naoya Sumi, Kenichiro Yamamoto, Kazuhiro Sakai

Publication date: 2 February 2010

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

zbMATH Keywords

Anosov diffeomorphismsperiodic pointshyperbolicityspecification property

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) (37D20) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Partially hyperbolic systems and dominated splittings (37D30)

Related Items (27)

Generic diffeomorphisms with weak limit shadowing ⋮ Eventual shadowing for chain transitive sets of $C^1$ generic dynamical systems ⋮ The barycenter property for robust and generic diffeomorphisms ⋮ Specification and partial hyperbolicity for flows ⋮ Specification property for topological spaces ⋮ On bi-Lyapunov stable homoclinic classes ⋮ Smooth TA-maps with robust shadowing are Axiom A ⋮ The weak specification property and distributional chaos ⋮ Flows with ergodic pseudo orbit tracing property ⋮ The specification property for flows from the robust and generic viewpoint ⋮ Unnamed Item ⋮ Gluing orbit property and partial hyperbolicity ⋮ Chain components with stably limit shadowing property are hyperbolic ⋮ Usual limit shadowable homoclinic classes of generic diffeomorphisms ⋮ Minimal sets and \(\omega\)-chaos in expansive systems with weak specification property ⋮ The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows ⋮ Expansive transitive sets for robust and generic diffeomorphisms ⋮ Diffeomorphisms with thes-limit shadowing property ⋮ Robustly chain transitive sets with orbital shadowing diffeomorphisms ⋮ Partial hyperbolicity and specification ⋮ The ergodic shadowing property from the robust and generic view point ⋮ Specification and thermodynamical properties of semigroup actions ⋮ Hyperbolicity, transitivity and the two-sided limit shadowing property ⋮ Measure-expansive diffeomorphisms ⋮ Weak specification properties and large deviations for non-additive potentials ⋮ Unstable entropies and dimension theory of partially hyperbolic systems ⋮ Hyperbolicity through stable shadowing for generic geodesic flows

Cites Work

• Unnamed Item
• Ergodic theory on compact spaces
• Pseudo-orbit tracing property and strong transversality of diffeomorphisms on closed manifolds
• An ergodic closing lemma
• Dynamics beyond uniform hyperbolicity. A global geometric and probabilistic perspective
• Periodic Points and Measures for Axiom a Diffeomorphisms
• Necessary Conditions for Stability of Diffeomorphisms

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