1.D.M.A., UMR 8553, école Normale Supérieure,Paris,France;2.Dipartimento di Matematica,Università degli Studi di Roma Tor Vergata,Rome,Italy;3.Department of Mathematical Sciences,University of Copenhagen,Copenhagen ?,Denmark
Abstract:
We prove exponential decay of correlations for a realistic model of piecewise hyperbolic flows preserving a contact form, in dimension three. This is the first time exponential decay of correlations is proved for continuous-time dynamics with singularities on a manifold. Our proof combines the second author’s version (Liverani in Ann Math 159:1275–1312, 2004) of Dolgopyat’s estimates for contact flows and the first author’s work with Gouëzel (J Mod Dyn 4:91–137, 2010) on piecewise hyperbolic discrete-time dynamics.
