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

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.

This paper has been significantly expanded and extended in the paper "Stochastic-like behaviour in nonuniformly expanding maps" math.DS/0409085