Mixing properties of a class of nonuniformly expanding maps. Application to Hölderian invariance principles.
Résumé
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 Hölder spaces for the partial sum process of Birkhoff sums of Hölder continuous observables. The results apply to a class of intermittent maps of the unit interval. For such a map, we also prove that the Hölder invariance principle remains true for BV observables.
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