Mixing for continuous time dynamical systems with infinite measure

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.

This paper was never submitted for publication and has been withdrawn. It is subsumed in our preprint "Operator renewal theory for continuous time dynamical systems with finite and infinite measure" arXiv:1404.2508 which covers finite measure continuous time systems in addition to the infinite measure case