Approximation properties on invariant measure and Oseledec splitting in non-uniformly hyperbolic systems

DOI10.1090/S0002-9947-08-04630-8zbMath1168.37006MaRDI QIDQ3617624

Geng Liu, Chao Liang, Wen Xiang Sun

Publication date: 30 March 2009

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

zbMATH Keywords

invariant measurehyperbolic periodic orbitnon-uniformly hyperbolic dynamical system

Mathematics Subject Classification ID

Entropy and other invariants, isomorphism, classification in ergodic theory (37A35) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Smooth ergodic theory, invariant measures for smooth dynamical systems (37C40) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (21)

Generalized fractal dimensions of invariant measures of full-shift systems over compact and perfect spaces: generic behavior ⋮ Conditions for dominated splittings ⋮ A note on approximation properties of the Oseledets splitting ⋮ Periodic measures are dense in invariant measures for residually finite amenable group actions with specification ⋮ Exponential rate of periodic points and metric entropy in nonuniformly hyperbolic systems ⋮ Lyapunov exponents and hyperbolic periodic orbits for endomorphisms ⋮ Some results on bundle systems for a countable discrete amenable group action ⋮ The Lyapunov exponents of \(C^{1}\) hyperbolic systems ⋮ Variational equalities of entropy in nonuniformly hyperbolic systems ⋮ Deviation property of periodic measures in \(C^1\) non-uniformly hyperbolic systems with limit domination ⋮ Periodic approximation of Oseledets subspaces for semi-invertible cocycles ⋮ Every expanding measure has the nonuniform specification property ⋮ Ergodic properties of systems with asymptotic average shadowing property ⋮ Topological features of flows with the reparametrized gluing orbit property ⋮ On the approximation of dynamical indicators in systems with nonuniformly hyperbolic behavior ⋮ Lyapunov exponents of hyperbolic measures and hyperbolic periodic orbits ⋮ Ergodic properties of invariant measures for C^1+α non-uniformly hyperbolic systems ⋮ On the density of periodic measures for piecewise monotonic maps and their coding spaces ⋮ Generic properties of invariant measures of full-shift systems over perfect Polish metric spaces ⋮ Uniform hyperbolic approximations of measures with non-zero Lyapunov exponents ⋮ Non-uniform hyperbolicity and non-uniform specification

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Certain ergodic properties of a differential system on a compact differentiable manifold
• Entropy and ergodic probability for differentiable dynamical systems and their bundle extensions
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Weakly almost periodic point and measure centre
• Characteristic spectrum for differential systems
• Periodic probability measures are dense in the set of invariant measures
• Lyapunov exponents of hyperbolic measures and hyperbolic periodic orbits
• FAMILIES OF INVARIANT MANIFOLDS CORRESPONDING TO NONZERO CHARACTERISTIC EXPONENTS
• LIAO STYLE NUMBERS OF DIFFERENTIAL SYSTEMS
• On Dynamical Systems With the Specification Property
• Genericity of zero Lyapunov exponents

This page was built for publication: Approximation properties on invariant measure and Oseledec splitting in non-uniformly hyperbolic systems