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

TL;DR

This paper investigates the mixing behavior of certain nonuniformly expanding maps with weak return time moments and establishes an invariance principle in Hölder spaces, applicable to intermittent maps and BV observables.

Contribution

It introduces new results on mixing rates and invariance principles for nonuniformly expanding maps with weak moment conditions, extending to intermittent maps and BV observables.

Findings

Proves Hölder invariance principle for nonuniformly expanding maps.

Shows invariance principle holds for BV observables in intermittent maps.

Establishes mixing properties under weak moment conditions.

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.