A note on statistical properties for nonuniformly hyperbolic systems with slow contraction and expansion

2014/11/30 by Ian Melbourne, Paulo Varandas
Mathematics · #math.DS #msc:37A50 #msc:37D25 #msc:37D50 #msc:60F17

paper · pdf

published as Stochastics & Dynamics 16 (2016) 1660012 (13 pages) · Final version

arxiv created 2016/03/10 · arxiv updated 2016/03/11

Abstract

We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time function is square-integrable, then we obtain the central limit theorem, the weak invariance principle, and an iterated version of the weak invariance principle.

Cited by

• Multidimensional non-uniform hyperbolicity, robust exponential mixing and the basin problem