# American Institute of Mathematical Sciences

May  2016, 36(5): 2585-2611. doi: 10.3934/dcds.2016.36.2585

## Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems

 1 Department of Mathematics, University of Southern California, Los Angeles, CA 90089 2 Department of Mathematics, Harvard-Westlake School, Studio City, CA 91604, United States

Received  December 2014 Revised  September 2015 Published  October 2015

We show that for systems that allow a Young tower construction with polynomially decaying correlations the return times to metric balls are in the limit Poisson distributed. We also provide error terms which are powers of logarithm of the radius. In order to get those uniform rates of convergence the balls centres have to avoid a set whose size is estimated to be of similar order. This result can be applied to non-uniformly hyperbolic maps and to any invariant measure that satisfies a weak regularity condition. In particular it shows that the return times to balls is Poissonian for SRB measures on attractors.
Citation: Nicolai T. A. Haydn, Kasia Wasilewska. Limiting distribution and error terms for the number of visits to balls in non-uniformly hyperbolic dynamical systems. Discrete & Continuous Dynamical Systems - A, 2016, 36 (5) : 2585-2611. doi: 10.3934/dcds.2016.36.2585
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