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Communications in Mathematical Physics, 206(1), 33–55p. (1999) DOI:10.1007/s002200050697

Statistics of Return Times: A General Framework and New Applications

M. Hirata, B. Saussol, S. Vaienti

In this paper we provide general estimates for the errors between the distribution of the first, and more generally, the Kth 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.