Hirata, Masaki; Saussol, Benoît; Vaienti, Sandro Statistics of return times: A general framework and new applications. (English) Zbl 0955.37001 Commun. Math. Phys. 206, No. 1, 33-55 (1999). 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. Reviewer: Ilya Pavlyukevitch (Berlin) Cited in 1 ReviewCited in 79 Documents MSC: 37A25 Ergodicity, mixing, rates of mixing 28D05 Measure-preserving transformations 37D20 Uniformly hyperbolic systems (expanding, Anosov, Axiom A, etc.) 37E05 Dynamical systems involving maps of the interval 60F05 Central limit and other weak theorems Keywords:measurable dynamical systems; strong mixing; return time; Poisson law PDFBibTeX XMLCite \textit{M. Hirata} et al., Commun. Math. Phys. 206, No. 1, 33--55 (1999; Zbl 0955.37001) Full Text: DOI