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Recurrence rate in rapidly mixing dynamical systems

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  • For measure preserving dynamical systems on metric spaces we study the time needed by a typical orbit to return back close to its starting point. We prove that when the decay of correlation is super-polynomial the recurrence rates and the pointwise dimensions are equal. This gives a broad class of systems for which the recurrence rate equals the Hausdorff dimension of the invariant measure.
    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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