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

2003/01/27 by Stefano Luzzatto, Luzzatto, Stefano
Mathematics · Physics and Astronomy · #37A25 #37D25 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #math-ph #math.DS #math.MP #math.PR #msc:37A25 #msc:37D25

paper · pdf · doi:10.48550/arxiv.math/0301319

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

arxiv created 2004/11/02 · arxiv updated 2009/11/30

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.

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