Fast decay of correlations of equilibrium states of open classes of   non-uniformly expanding maps and potentials
  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. 
Alexander Arbieto and Carlos Matheus