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

Final minor changes

References in corpus (3)

• Strong invariance principles with rate for "reverse" martingales and applications
• Polynomial decay of correlations for flows, including Lorentz gas examples
• A local limit theorem with speed of convergence for Euclidean algorithms and diophantine costs

Cited by in corpus (6)

• Multiscale systems, homogenization, and rough paths
• Expansions in the local and the central limit theorems for dynamical systems
• Polynomial decay of correlations for flows, including Lorentz gas examples
• Homogenization of Fully-Coupled Chaotic Fast-Slow Systems via Intermediate Stochastic Regularization
• Martingale approximations and anisotropic Banach spaces with an application to the time-one map of a Lorentz gas
• Robust Exponential Mixing and Convergence to Equilibrium for Singular Hyperbolic Attracting Sets