Equilibrium states for natural extensions of non-uniformly expanding local homeomorphisms

Existence, Uniqueness and Stability of Equilibrium States for Non-uniformly Expanding Maps

We prove existence of finitely many ergodic equilibrium states for a large class of non-uniformly expanding local homeomorphisms on compact manifolds and Hölder continuous potentials with not very large oscillation. No Markov structure is assumed. If the transformation is topologically mixing there is a unique equilibrium state, it is exact and satisfies a non-uniform Gibbs property. Under mild...

Invariant manifolds and equilibrium states for non-uniformly hyperbolic horseshoes

In this paper we consider horseshoes containing an orbit of homoclinic tangency accumulated by periodic points. We prove a version of the Invariant Manifolds Theorem, construct finite Markov partitions and use them to prove the existence and uniqueness of equilibrium states associated to Hölder continuous potentials.

Subexponential decay of correlations for compact group extensions of non-uniformly expanding systems

We show that the renewal theory developed by Sarig and Gouëzel in the context of nonuniformly expanding dynamical systems applies also to the study of compact group extensions of such systems. As a consequence, we obtain results on subexponential decay of correlations for equivariant Hölder observations.

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 Hölder continuous potentials. The approach used in this paper is the spectral analysis of the Ruelle-PerronFrobenius transfer operator. More precisely, we combine the expanding features of the eigenmeasures of the transfer ...

Random Perturbations of Non-Uniformly Expanding Maps