Mixing properties of a class of nonuniformly expanding maps. Application to H{\"o}lderian invariance principles

Abstract

We study the mixing properties of a class of nonuniformly expanding maps when the return time to the basis has a weak moment of order p >1, up to a slowly varying function. From these computations, we deduce an invariance principle in H{\"o}lder spaces for the partial sum process of Birkhoff sums of H{\"o}lder continuous observables. The results apply to a class of intermittent maps of the unit interval. For such a map, we also prove that the H{\"o}lder invariance principle remains true for BV observables.