Statistics of return times: A general framework and new applications

In this paper we provide general estimates for the errors between the distr ibution of the first, and more generally, the K-th return time (suitably re scaled) and the Poisson law for measurable dynamical systems. In the case t hat the system exhibits strong mixing properties, these bounds are explicit ly expressed in terms of the speed of mixing. Using these approximations, t he Poisson law is finally proved to hold for a large class of non hyperboli c systems on the interval.