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arXiv · 0805.2760

Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps

Paulo Varandas
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Abstract

We study decay of correlations, the asymptotic distribution of hitting times and fluctuations of the return times for a robust class of multidimensional non-uniformly hyperbolic transformations. Oliveira and Viana [15] proved that there is a unique equilibrium state for a large class of non- uniformly expanding transformations and Holder continuous potentials with small variation. For an open class of potentials with small variation, we prove quasi-compactness of the Ruelle-Perron-Frobenius operator in a space $V_θ$ of functions with essential bounded variation that strictly contain Holder continuous observables. We deduce that the equilibrium states have exponential decay of correlations. Furthermore, we prove exponential asymptotic distribu- tion of hitting times and log-normal fluctuations of the return times around the average given by the metric entropy.

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Paulo Varandas. 2008-05-18. Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps. https://doi.org/10.1007/s10955-008-9639-3

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