Statistics of Return Times:¶A General Framework and New Applications

Abstract:

In this paper we provide general estimates for the errors between the distribution of the first, and more generally, the K ^th return time (suitably rescaled) and the Poisson law for measurable dynamical systems. In the case that the system exhibits strong mixing properties, these bounds are explicitly expressed in terms of the speed of mixing. Using these approximations, the Poisson law is finally proved to hold for a large class of non hyperbolic systems on the interval.