Superpolynomial and polynomial mixing for semiflows and flows

TL;DR

This paper reviews decay of correlations in nonuniformly expanding and hyperbolic flows, providing proofs for semiflows and discussing applications to various chaotic dynamical systems.

Contribution

It offers a self-contained proof for superpolynomial and polynomial decay in semiflows and summarizes recent results for flows, including applications to physical models.

Findings

Superpolynomial decay of correlations for semiflows

Polynomial decay of correlations for nonuniformly hyperbolic flows

Applications to Lorenz attractors and Lorentz gas models

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 Balint and Butterley). Applications include intermittent solenoidal flows, suspended Henon attractors, Lorenz attractors, and various Lorentz gas models including the infinite horizon Lorentz gas.