Decay of correlations for nonuniformly expanding systems with general return times

TL;DR

This paper provides a unified and elementary approach to analyze the decay of correlations in nonuniformly expanding systems with general return times, broadening applicability under mild conditions.

Contribution

It introduces a simplified, unified method for studying decay of correlations that applies to general integrable return time functions in nonuniformly expanding systems.

Findings

Results hold for general integrable return time functions

Method is more elementary than previous approaches

Applicable under mild conditions on the inducing scheme

Abstract

We give a unified treatment of decay of correlations for nonuniformly expanding systems with a good inducing scheme. In addition to being more elementary than previous treatments, our results hold for general integrable return time functions under fairly mild conditions on the inducing scheme.