Markov Approximations and Decay of Correlations for Anosov Flows

Abstract

We develop Markov approximations for very general suspension flows. Based on this, we obtain a stretched exponential bound on time correlation functions for 3-D Anosov flows that verify ‘uniform nonintegrability of foliations’. These include contact Anosov flows and geodesic flows on compact surfaces of variable negative curvature. Our bound on correlations is stable under small smooth perturbations.