Mixing for continuous time dynamical systems with infinite measure

TL;DR

This paper develops operator renewal theory for flows to analyze mixing properties in infinite measure dynamical systems, covering examples like suspensions over complex maps and semiflows with indifferent orbits, providing asymptotics and mixing rates.

Contribution

It introduces a new operator renewal framework for infinite measure flows, enabling analysis of mixing and asymptotics in complex dynamical systems.

Findings

Established mixing results for a broad class of infinite measure semiflows

Derived higher order asymptotics and mixing rates

Applied theory to systems like complex rational maps and semiflows with indifferent periodic orbits

Abstract

We develop operator renewal theory for flows and apply this to infinite ergodic theory. In particular we obtain results on mixing for a large class of infinite measure semiflows. Examples of systems covered by our results include suspensions over parabolic rational maps of the complex plane, and nonuniformly expanding semiflows with indifferent periodic orbits. In some cases, we obtain higher order asymptotics and rates of mixing.