Good inducing schemes for uniformly hyperbolic flows, and applications to exponential decay of correlations

Ann. Henri Poincaré. Appeared online April 2024.

Ian Melbourne and Paulo Varandas

Abstract

Given an Axiom A attractor for a C^1+α flow (α>0), we construct a countable Markov extension with exponential return times in such a way that the inducing set is a smoothly embedded unstable disk. This avoids technical issues concerning irregularity of boundaries of Markov partition elements and enables an elementary approach to certain questions involving exponential decay of correlations for SRB measures.