Rates of mixing for nonMarkov infinite measure semiflows

TL;DR

This paper introduces a new abstract framework to determine optimal mixing rates and higher order asymptotics for infinite measure semiflows, extending beyond the Markov and uniformly expanding cases.

Contribution

It develops a general method for analyzing mixing in infinite measure semiflows, including non-Markov and non-uniformly expanding systems, which were previously inaccessible.

Findings

Established mixing rates for semiflows over non-Markov Pomeau-Manneville maps.

Derived mixing rates for semiflows over Collet-Eckmann maps with nonintegrable roof functions.

Extended the theory of infinite measure semiflows beyond classical Markov assumptions.

Abstract

We develop an abstract framework for obtaining optimal rates of mixing and higher order asymptotics for infinite measure semiflows. Previously, such results were restricted to the situation where there is a first return Poincar\'e map that is uniformly expanding and Markov. As illustrations of the method, we consider semiflows over nonMarkov Pomeau-Manneville intermittent maps with infinite measure, and we also obtain mixing rates for semiflows over Collet-Eckmann maps with nonintegrable roof function.