Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps

Details Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps

2008-05-18

arxiv.org/abs/0805.2760v1

Mathematics

Dynamical Systems

24 pages

Scientific paper

10.1007/s10955-008-9639-3

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 $V_\theta$ 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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