Statistics of return times: A general framework and new applications (Q1817755)

The authors provide general estimates for the error 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 nonhyperbolic systems on the interval.