Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results

TL;DR

This paper surveys recent advances in understanding how correlations decay in non-uniformly expanding maps, linking decay rates to geometric features of the systems.

Contribution

It provides a comprehensive overview of recent results on decay of correlations and explores the geometric reasons behind different decay rates.

Findings

Decay rates vary across systems due to geometric differences

Recent results establish links between dynamics and geometry

The survey highlights key methods and open questions

Abstract

We discuss recent results on decay of correlations for non-uniformly expanding maps. Throughout the discussion, we address the question of why different dynamical systems have different rates of decay of correlations and how this may reflect underlying geometrical characteristics of the system.