Fast decay of correlations of equilibrium states of open classes of non-uniformly expanding maps and potentials

Details Fast decay of correlations of equilibrium states of open classes of non-uniformly expanding maps and potentials Fast decay of correlations of equilibrium states of open classes of non-uniformly expanding maps and potentials

2006-03-27

arxiv.org/abs/math/0603629v1

Mathematics

Dynamical Systems

44 pages

Scientific paper

We study the existence, uniqueness and rate of decay of correlation of equilibrium measures associated to robust classes of non-uniformly expanding local diffeomorphisms and H\"older continuous potentials. The approach used in this paper is the spectral analysis of the Ruelle-Perron-Frobenius transfer operator. More precisely, we combine the expanding features of the eigenmeasures of the transfer operator with a Lasota-Yorke type inequality to prove the existence of an unique equilibrium measure with fast decay of correlations.

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