Statistics of closest returns for some non-uniformly hyperbolic systems

Details Statistics of closest returns for some non-uniformly hyperbolic systems Statistics of closest returns for some non-uniformly hyperbolic systems

1999-04-23

arxiv.org/abs/math/9904134v1

Mathematics

Dynamical Systems

Scientific paper

For non uniformly hyperbolic maps of the interval with exponential decay of correlations we prove that the law of closest return to a given point when suitably normalized is almost surely asymptotically exponential. A similar result holds when the reference point is the initial point of the trajectory. We use the framework for non uniformly hyperbolic dynamical systems developed by L.S.Young.

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