Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure

TL;DR

This paper establishes mixing properties and rates for toral extensions of nonuniformly expanding maps with subexponential decay, applicable in both finite and infinite measure contexts, under a Dolgopyat-type nonexistence condition.

Contribution

It extends existing mixing results to toral extensions of nonuniformly expanding maps, including infinite measure cases, under a Dolgopyat-type condition.

Findings

Mixing and mixing rates are proven for toral extensions.

Results apply to both finite and infinite measure settings.

Conditions under which mixing properties hold are identified.

Abstract

We prove results on mixing and mixing rates for toral extensions of nonuniformly expanding maps with subexponential decay of correlations. Both the finite and infinite measure settings are considered. Under a Dolgopyat-type condition on nonexistence of approximate eigenfunctions, we prove that existing results for (possibly nonMarkovian) nonuniformly expanding maps hold also for their toral extensions.