Recurrence rate in rapidly mixing dynamical systems

Details Recurrence rate in rapidly mixing dynamical systems Recurrence rate in rapidly mixing dynamical systems

2004-12-10

arxiv.org/abs/math/0412211v1

Mathematics

Dynamical Systems

Scientific paper

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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