Operator renewal theory for continuous time dynamical systems with finite and infinite measure
Monatshefte für Mathematik
Springer Verlag (Germany)
This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.
Reason for embargo
We develop operator renewal theory for flows and apply this to obtain results on mixing and rates of mixing for a large class of finite and 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 the finite measure case, the emphasis is on obtaining sharp rates of decorrelations, extending results of Gou\"ezel and Sarig from the discrete time setting to continuous time. In the infinite measure case, the primary question is to prove results on mixing itself, extending our results in the discrete time setting. In some cases, we obtain also higher order asymptotics and rates of mixing.
The research of IM was supported in part by EPSRC Grant EP/F031807/1 (held at the University of Surrey) and by the European Advanced Grant StochExtHomog (ERC AdG 320977). The research of DT was supported in part by the European Advanced Grant MALADY (ERC AdG 246953). IM and DT are grateful to the Centre International de Rencontres Math´ematiques for funding the Research in Pairs topic “Infinite Ergodic Theory”, Luminy, August 2012, where part of this research was carried out.