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

Annales Henri Lebesgue 4 (2021) 407-451

Henk Bruin, Ian Melbourne and Dalia Terhesiu

Abstract

Gouëzel 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.

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Typo: In the example Dispersing billiards with vanishing curvature in Section 1.1, reference [56] should be [16]. (References to [56] later in the paper are correct.)