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

Alexander Arbieto·Carlos Matheus
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Abstract

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 Hölder 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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Alexander Arbieto, Carlos Matheus. 2006-03-27. Fast decay of correlations of equilibrium states of open classes of non-uniformly expanding maps and potentials. https://arxiv.org/abs/math/0603629

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