Exponential Decay of Correlations for Piecewise Cone Hyperbolic Contact Flows

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 GouA << zel (J Mod Dyn 4:91-137, 2010) on piecewise hyperbolic discrete-time dynamics