Recurrence rate in rapidly mixing dynamical systems

Benoit Saussol

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Recurrence rate in rapidly mixing dynamical systems

Benoit Saussol

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Abstract

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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Benoit Saussol. 2004-12-10. Recurrence rate in rapidly mixing dynamical systems. https://arxiv.org/abs/math/0412211

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