Mixing rates for symplectic almost Anosov maps

Abstract

We establish sharp bounds on the mixing rates of a class of two dimensional non-uniformly hyperbolic symplectic maps. This provides a primer on how to investigate such questions in a concrete example and, at the same time, it solves a controversy between previous rigorous results and numerical experiments. P.E.; while C.L. was partially supported by the PRIN Grant Regular and stochastic behaviour in dynamical systems (PRIN 2017S35EHN).