Random perturbations of non - uniformly expanding maps ∗

Random Perturbations of Non-Uniformly Expanding Maps

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...

Large Deviations Bounds for Non-uniformly Hyperbolic Maps and Weak Gibbs Measures

We establish bounds for the measure of deviation sets associated to continuous observables with respect to weak Gibbs measures. Under some mild assumptions, we obtain upper and lower bounds for the measure of deviation sets of some non-uniformly expanding maps, including quadratic maps and robust multidimensional non-uniformly expanding local diffeomorphisms.

Extreme Value Distributions for some classes of Non-Uniformly Partially Hyperbolic Dynamical Systems

In this note, we obtain verifiable sufficient conditions for the extreme value distribution for a certain class of skew product extensions of non-uniformly hyperbolic base maps. We show that these conditions, formulated in terms of the decay of correlations on the product system and the measure of rapidly returning points on the base, lead to a distribution for the maximum of Φ(p) = − log(d(p, ...

Decay of correlations for non-Hölder observables

We consider the general question of estimating decay of correlations for non-uniformly expanding maps, for classes of observables which are much larger than the usual class of Hölder continuous functions. Our results give new estimates for many non-uniformly expanding systems, including Manneville-Pomeau maps, many one-dimensional systems with critical points, and Viana maps. In many situations...