Benoit Saussol (Brest)

Title: Spatio-temporal Poisson process for visits to small sets in hyperbolic dynamics

Abstract: (joint work with Francoise Pene) 
We study a recurrence property of a finite measure preserving dynamical system (X,T,m). Given a small set A, we are interested in the process obtained from recording the successive times n of visits to A and the
position T^n(x) in A of the orbit, in the limit where m(A)->0. We obtain a convergence of this process, suitably normalized, to a Poisson point process in time and space under some decorrelation condition. We present some applications to hyperbolic maps and SRB measures and some billiards. We also consider the case of a neighborhood of a periodic point.