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

2016/05/05 by Vaienti, Sandro, Zhang, Hong-Kun
#37A25 #37D50 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1605.01793

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.

Related

• Improved estimates of statistical properties in some non-uniformly hyperbolic dynamical systems
• Mixing for some non-uniformly hyperbolic systems
• Recurrence times and rates of mixing for invertible dynamical systems
• Almost sure rates of mixing for partially hyperbolic attractors
• Decay of correlations for non-Holder observables