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Pré-Publication, Document De Travail Année : 2004

Recurrence rate in rapidly mixing dynamical systems

Résumé

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.
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Dates et versions

hal-00003516 , version 1 (10-12-2004)

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Benoit Saussol. Recurrence rate in rapidly mixing dynamical systems. 2004. ⟨hal-00003516⟩
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