Optimal bounds for decay of correlations and {\alpha}-mixing for nonuniformly hyperbolic dynamical systems
Dynamical Systems
2019-06-28 v5
Abstract
We investigate the decay rates of correlations for nonuniformly hyperbolic systems with or without singularities, on piecewise H\"older 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.
Keywords
Cite
@article{arxiv.1605.01793,
title = {Optimal bounds for decay of correlations and {\alpha}-mixing for nonuniformly hyperbolic dynamical systems},
author = {Sandro Vaienti and Hong-Kun Zhang},
journal= {arXiv preprint arXiv:1605.01793},
year = {2019}
}