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

Arbieto, Alexander; Matheus, Carlos

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

Authors

Description

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.
44 pages