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February  2006, 15(1): 1-20. doi: 10.3934/dcds.2006.15.1

A survey of recent results on some statistical features of non-uniformly expanding maps

José F. Alves 1,

1. 

CMUP, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

Received  December 2004 Revised  November 2005 Published  February 2006

The aim of this paper is to present a survey of recent results on the statistical properties of non-uniformly expanding maps on finite-dimensional Riemannian manifolds. We will mostly focus on the existence of SRB measures, continuity of the SRB measure and its entropy, decay of correlations, and stochastic stability.
Keywords: stochastic stability, statistical stability, decay of correlations, SRB measure, continuity of entropy..
Mathematics Subject Classification: Primary: 37-02, Secondary: 37A25, 37A35, 37C4.
Citation: José F. Alves. A survey of recent results on some statistical features of non-uniformly expanding maps. Discrete & Continuous Dynamical Systems - A, 2006, 15 (1) : 1-20. doi: 10.3934/dcds.2006.15.1
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