Sharp polynomial bounds on decay of correlations for multidimensional nonuniformly hyperbolic systems and billiards

Abstract

Gouezel and Sarig introduced operator renewal theory as a method to prove sharp results on polynomial decay of correlations for certain classes of nonuniformly expanding maps. In this paper, we apply the method to planar dispersing billiards and multidimensional nonMarkovian intermittent maps.

Final version. To appear in Annales Henri Lebesgue (Some gaps fixed from previous "final" version; main theorems and examples unchanged.)