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

José F. Alves

doi:10.3934/dcds.2006.15.1

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2006, Volume 15, Issue 1: 1-20. Doi: 10.3934/dcds.2006.15.1

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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

Received: December 2004

Revised: November 2005

Published: March 2006

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Abstract

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.

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Mathematics Subject Classification: Primary: 37-02, Secondary: 37A25, 37A35, 37C40.

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