Superpolynomial and polynomial mixing for semiflows and flows

Abstract

We give a review of results on superpolynomial decay of correlations, and polynomial decay of correlations, for nonuniformly expanding semiflows and nonuniformly hyperbolic flows. A self-contained proof is given for semiflows. Results for flows are stated without proof (the proofs are contained in separate joint work with Bálint and Butterley). Applications include intermittent solenoidal flows, suspended Hénon attractors, Lorenz attractors and singular hyperbolic attractors, and various Lorentz gas models including the infinite horizon Lorentz gas.