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

Ian Melbourne; Paulo Varandas

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

Dynamical Systems 2025-06-17 v3

Authors: Ian Melbourne , Paulo Varandas

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.

Keywords

axiom a attractor uniformly hyperbolic flows countable markov extension exponential decay of correlations srb measures inducing schemes

Cite

@article{arxiv.2302.12363,
  title  = {Good inducing schemes for uniformly hyperbolic flows, and applications to exponential decay of correlations},
  author = {Ian Melbourne and Paulo Varandas},
  journal= {arXiv preprint arXiv:2302.12363},
  year   = {2025}
}

Comments

Added the standard argument relating UNI to joint nonintegrability. Corrected a few typos

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

Abstract

Keywords

Cite

Comments

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