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Statistics of return times: A general framework and new applications. (English) Zbl 0955.37001

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.

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
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