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arXiv · 1605.01793

Optimal bounds for decay of correlations and {\alpha}-mixing for nonuniformly hyperbolic dynamical systems

Sandro Vaienti·Hong-Kun Zhang
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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.

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Sandro Vaienti, Hong-Kun Zhang. 2016-05-05. Optimal bounds for decay of correlations and {\alpha}-mixing for nonuniformly hyperbolic dynamical systems. https://arxiv.org/abs/1605.01793

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