Fast decay of correlations of equilibrium states of open classes of non-uniformly expanding maps and potentials
Carlos Matheus | Arbieto, Alexander
Equilibrium states | Ruelle-Perron-Frobenius transfer operator | non-uniform expansion | Lasota-Yorke inequality | decay of correlations
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 Hólder 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.