VIVIANE BALADI and CARLANGELO LIVERANI
                                                       
                                                       
                  EXPONENTIAL DECAY OF CORRELATIONS FOR PIECEWISE CONE HYPERBOLIC CONTACT FLOWS
           
                                                                      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 [28] of Dolgopyat's estimates for contact flows and the first author's work with Gouezel [5] on piecewise hyperbolic discrete-time dynamics.