Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences

DOI10.1215/00127094-2009-011zbMath1170.37006arXivmath/0703670OpenAlexW1989088418MaRDI QIDQ1012322

Sébastien Gouëzel

Publication date: 16 April 2009

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703670

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Ergodic theorems, spectral theory, Markov operators (37A30) Dynamical systems and their relations with probability theory and stochastic processes (37A50) Partially hyperbolic systems and dominated splittings (37D30) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25)

Related Items (9)

Berry-Esseen bound and precise moderate deviations for products of random matrices ⋮ Limit theorems for fast-slow partially hyperbolic systems ⋮ Skew products, quantitative recurrence, shrinking targets and decay of correlations ⋮ A local limit theorem for a transient chaotic walk in a frozen environment ⋮ Stable laws and spectral gap properties for affine random walks ⋮ Exponential decay of correlations for Gibbs measures and semiflows over \(C^{1+\alpha }\) piecewise expanding maps ⋮ Asymptotic Counting in Conformal Dynamical Systems ⋮ Sharp connections between Berry-Esseen characteristics and Edgeworth expansions for stationary processes ⋮ Exponential mixing for skew products with discontinuities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Classifying the isometric extensions of a Bernoulli shift
• On mixing properties of compact group extensions of hyperbolic systems
• Exponential mixing for the Teichmüller flow
• Théorèmes limites pour une classe de chaînes de Markov et applications aux difféomorphismes d'Anosov. (Limit theorems for a class of Markov chains and applications to Anosov diffeomorphisms)
• On decay of correlations in Anosov flows
• Statistical properties of dynamical systems with some hyperbolicity
• Recurrence times and rates of mixing
• Subexponential decay of correlations
• Central limit theorem and stable laws for intermittent maps
• SRB measures for partially hyperbolic systems whose central direction is mostly expanding
• Euclidean algorithms are Gaussian
• Large deviation asymptotics for Anosov flows
• Berry--Esseen theorem and local limit theorem for non uniformly expanding maps
• Markov structures and decay of correlations for non-uniformly expanding dynamical systems
• Error terms for closed orbits of hyperbolic flows
• Spectrum of the Ruelle operator and exponential decay of correlations for open billiard flows
• Expanding maps on Cantor sets and analytic continuation of zeta functions
• Decay of correlations for nonuniformly expanding systems
• LIMIT THEOREMS FOR COUPLED INTERVAL MAPS
• Actions of large semigroups and random walks on isometric extensions of boundaries
• Physical measures for infinite-modal maps
• On the Bernoulli nature of systems with some hyperbolic structure
• Decay of correlations in one-dimensional dynamics
• Limit theorems for partially hyperbolic systems
• Strong statistical stability of non-uniformly expanding maps
• Exponential decay of correlations for surface semi-flows without finite Markov partitions
• Precise counting results for closed orbits of Anosov flows
• Sur un Theoreme Spectral et son Application aux Noyaux Lipchitziens
• Decay of correlations in suspension semi-flows of angle-multiplying maps
• Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness

This page was built for publication: Local limit theorem for nonuniformly partially hyperbolic skew-products and Farey sequences