Exponential rate of periodic points and metric entropy in nonuniformly hyperbolic systems

DOI10.1016/j.jmaa.2015.09.044zbMath1377.37052OpenAlexW2173136698MaRDI QIDQ891392

Yun Yang, Gang Liao, Wen Xiang Sun

Publication date: 17 November 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2015.09.044

zbMATH Keywords

periodic pointmetric entropyweak shadowing property

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Orbit growth in dynamical systems (37C35) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Topological entropy (37B40) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (2)

Pressure and exponential rate over periodic orbits ⋮ Horseshoes for \(\mathcal{C}^{1+\alpha}\) mappings with hyperbolic measures

Cites Work

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• Continuity properties of entropy
• Bernoulli diffeomorphisms on surfaces
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Periodic probability measures are dense in the set of invariant measures
• Large deviations, Gibbs measures and closed orbits for hyperbolic flows
• Generic properties of invariant measures for Axiom A diffeomorphisms
• Variational equalities of entropy in nonuniformly hyperbolic systems
• Metric entropy and the number of periodic points
• Lyapunov exponents of hyperbolic measures and hyperbolic periodic orbits
• Approximation properties on invariant measure and Oseledec splitting in non-uniformly hyperbolic systems
• Limit shadowing property
• Periodic Points and Measures for Axiom a Diffeomorphisms

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