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

## TL;DR

This paper constructs a smooth Markov extension for Axiom A attractors in hyperbolic flows, facilitating elementary proofs of exponential decay of correlations for SRB measures.

## Contribution

It introduces a new method to build Markov extensions with exponential return times using smooth unstable disks, simplifying analysis of decay of correlations.

## Key findings

- Constructed a countable Markov extension with exponential return times.
- Enabled elementary proofs of exponential decay of correlations.
- Avoided boundary irregularity issues in Markov partitions.

## Abstract

Given an Axiom A attractor for a $C^{1+\alpha}$ flow ($\alpha>0$), 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.