Ergodic properties of invariant measures for C1+α non-uniformly hyperbolic systems

DOI10.1017/S0143385711000940zbMath1278.37037arXiv1011.5300MaRDI QIDQ4928740

Chao Liang, Xue Ting Tian, Wen Xiang Sun

Publication date: 18 June 2013

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

Full work available at URL: https://arxiv.org/abs/1011.5300

zbMATH Keywords

ergodicityhyperbolic measuresshadowing lemmaspecification propertyPesin theory

Mathematics Subject Classification ID

Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (17)

Packing Entropy of Saturated Sets for Nonuniformly Hyperbolic Systems ⋮ Abundance of wild historic behavior ⋮ Upper capacity entropy and packing entropy of saturated sets for amenable group actions ⋮ Topological structures on saturated sets, optimal orbits and equilibrium states ⋮ Preimage pressure on subsets and multifractal analysis ⋮ On the topological entropy of saturated sets for amenable group actions ⋮ Variational equalities of entropy in nonuniformly hyperbolic systems ⋮ Preimage entropy and stable entropy on subsets ⋮ Multifractal analysis of ergodic averages in some non-uniformly hyperbolic systems ⋮ Transitively-saturated property, Banach recurrence and Lyapunov regularity ⋮ Distributional chaos in multifractal analysis, recurrence and transitivity ⋮ Ergodic properties of systems with asymptotic average shadowing property ⋮ Topological pressure for the completely irregular set of Birkhoff averages ⋮ On the limit quasi-shadowing property ⋮ Non-uniform hyperbolicity and non-uniform specification ⋮ Unstable entropies and dimension theory of partially hyperbolic systems ⋮ High pointwise emergence via saturated sets

Cites Work

• Unnamed Item
• Unnamed Item
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Ergodic theory on compact spaces
• Periodic probability measures are dense in the set of invariant measures
• Generic properties of invariant measures for Axiom A diffeomorphisms
• Approximation properties on invariant measure and Oseledec splitting in non-uniformly hyperbolic systems
• Genericity of zero Lyapunov exponents
• On the topological entropy of saturated sets
• Periodic Orbits for Hyperbolic Flows

This page was built for publication: Ergodic properties of invariant measures for C^1+α non-uniformly hyperbolic systems