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 C1+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.

pdf file, link to journal version

Typos: There are some minor inaccuracies in the proof of Lemma 2.9:

To ensure disjointness, δ0 in claim (**) should be δ0/2. So in the statement of the lemma, need to choose ε<δ0/4. Should also shrink δ (second line of proof) so that C3(3δ)α<δ0/4.

When applying (2.2), the constant C3 should be C2.

Here is a file showing the changes.