Non-uniform hyperbolicity and non-uniform specification

DOI10.1090/S0002-9947-2013-05819-9zbMath1352.37019arXiv1102.1652MaRDI QIDQ2847040

Krerley Oliveira, Xue Ting Tian

Publication date: 4 September 2013

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

Full work available at URL: https://arxiv.org/abs/1102.1652

zbMATH Keywords

Lyapunov exponentsshadowing propertyhyperbolic measuresdominated splittingPesin theory

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Orbit growth in dynamical systems (37C35) Dynamical systems with hyperbolic orbits and sets (37D05) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (8)

Topological entropy of level sets of empirical measures for non-uniformly expanding maps ⋮ Specification and partial hyperbolicity for flows ⋮ Periodic measures are dense in invariant measures for residually finite amenable group actions with specification ⋮ Topological structures on saturated sets, optimal orbits and equilibrium states ⋮ The gluing orbit property, uniform hyperbolicity and large deviations principles for semiflows ⋮ Topological features of flows with the reparametrized gluing orbit property ⋮ Partial hyperbolicity and specification ⋮ Specification and thermodynamical properties of semigroup actions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Livšic theorem for matrix cocycles
• Non-uniform specification and large deviations for weak Gibbs measures
• A note on periodic points for ergodic toral automorphisms
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• A generalized shadowing lemma
• Periodic probability measures are dense in the set of invariant measures
• Pseudo-orbit shadowing in the \(C^1\) topology
• Generic properties of invariant measures for Axiom A diffeomorphisms
• Exponential closing property and approximation of Lyapunov exponents of linear cocycles
• Decomposition of dynamical systems on an interval
• 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
• On the weaker forms of the specification property and their applications
• A variational principle for topological pressure for certain non-compact sets
• Specification on the interval
• Ergodic properties of invariant measures for C^1+α non-uniformly hyperbolic systems
• On the topological entropy of saturated sets
• Thermodynamical formalism for robust classes of potentials and non-uniformly hyperbolic maps
• Every expanding measure has the nonuniform specification property
• Periodic Orbits for Hyperbolic Flows
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms
• Invariant manifolds

This page was built for publication: Non-uniform hyperbolicity and non-uniform specification