March  2006, 16(1): 19-46. doi: 10.3934/dcds.2006.16.19

Decay of correlations for non-Hölder observables

1. 

Mathematics Institute, University of Warwick, Gibbet Hill Road, Coventry, CV5 7AL, United Kingdom

Received  January 2005 Revised  December 2005 Published  June 2006

We consider the general question of estimating decay of correlations for non-uniformly expanding maps, for classes of observables which are much larger than the usual class of Hölder continuous functions. Our results give new estimates for many non-uniformly expanding systems, including Manneville-Pomeau maps, many one-dimensional systems with critical points, and Viana maps . In many situations, we also obtain a Central Limit Theorem for a much larger class of observables than usual.
    Our main tool is an extension of the coupling method introduced by L.-S. Young for estimating rates of mixing on certain non-uniformly expanding tower maps.
Citation: Vincent Lynch. Decay of correlations for non-Hölder observables. Discrete and Continuous Dynamical Systems, 2006, 16 (1) : 19-46. doi: 10.3934/dcds.2006.16.19
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