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

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.

arXiv comment44 pages

References in corpus (1)

• Equilibrium States for Random Non-uniformly Expanding Maps

Cited by in corpus (4)

• Correlation decay and recurrence estimates for some robust nonuniformly hyperbolic maps
• Existence, uniqueness and stability of equilibrium states for non-uniformly expanding maps
• Topological pressure for one-dimensional holomorphic dynamical systems
• Large deviations bound for semiflows over a non-uniformly expanding base