Slow rates of mixing for dynamical systems with hyperbolic structures

DOI10.1007/s10955-008-9482-6zbMath1144.82324OpenAlexW2002495491MaRDI QIDQ927197

Vilton Pinheiro, José F. Alves

Publication date: 4 June 2008

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-008-9482-6

zbMATH Keywords

central limit theoremdecay of correlationsrecurrence times

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

Related Items (17)

Smooth approximation of stochastic differential equations ⋮ Decay of correlations for invertible maps with non-Hölder observables ⋮ Iterated invariance principle for slowly mixing dynamical systems ⋮ Superpolynomial and polynomial mixing for semiflows and flows ⋮ Exponential decay of random correlations for random Anosov systems mixing on fibers ⋮ Poisson law for some non-uniformly hyperbolic dynamical systems with polynomial rate of mixing ⋮ Martingale-coboundary decomposition for families of dynamical systems ⋮ Gibbs-Markov structures and limit laws for partially hyperbolic attractors with mostly expanding central direction ⋮ Statistical properties of diffeomorphisms with weak invariant manifolds ⋮ Rate of convergence in the weak invariance principle for deterministic systems ⋮ Almost sure rates of mixing for partially hyperbolic attractors ⋮ Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards ⋮ Quenched decay of correlations for slowly mixing systems ⋮ Gibbs-Markov-Young structures with (stretched) exponential tail for partially hyperbolic attractors ⋮ Young towers for product systems ⋮ Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems ⋮ SRB measures and Young towers for surface diffeomorphisms

Cites Work

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• First return map and invariant measures
• Ergodic properties of invariant measures for piecewise monotonic transformations
• Statistical properties of dynamical systems with some hyperbolicity
• Recurrence times and rates of mixing
• Multidimensional nonhyperbolic attractors
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• Decay of correlations for nonuniformly expanding systems
• A Measure Associated with Axiom-A Attractors
• GIBBS MEASURES IN ERGODIC THEORY
• Equilibrium states and the ergodic theory of Anosov diffeomorphisms

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