Optimal bounds for decay of correlations and α-mixing for nonuniformly hyperbolic dynamical systems

Abstract

We investigate the decay rates of correlations for nonuniformly hyperbolic systems with or without singularities, on piecewise Hölder observables. By constructing a new scheme of coupling methods using the probability renewal theory, we obtain the optimal bounds for decay rates of correlations for a large class of such observables. We also establish the alpha-mixing property for time series generated by these systems, which leads to a vast ranges of limiting theorems. Our results apply to rather general hyperbolic systems with singularities, including Bunimovich flower billiards, semidispersing billiards on a rectangle and billiards with cusps, and other nonuniformly hyperbolic maps.

References in corpus (1)

• Spatial structure of Sinai-Ruelle-Bowen measures

Cited by in corpus (4)

• Elliptic Flowers: simply connected billiard tables with chaotic or non-chaotic flows moving around chaotic or non-chaotic cores
• Markov partition and Thermodynamic Formalism for Hyperbolic Systems with Singularities
• On Coupling Lemma and Stochastic Properties with Unbounded Observables for 1-d Expanding Maps
• Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems