February  2006, 15(1): 259-267. doi: 10.3934/dcds.2006.15.259

Recurrence rate in rapidly mixing dynamical systems

1. 

Département de Mathématiques - CNRS UMR 6205, Université de Bretagne Occidentale, 6 Avenue le Gorgeu, CS 93837, 29238 Brest cedex 3, France

Received  November 2004 Revised  July 2005 Published  February 2006

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.
Citation: Benoît Saussol. Recurrence rate in rapidly mixing dynamical systems. Discrete and Continuous Dynamical Systems, 2006, 15 (1) : 259-267. doi: 10.3934/dcds.2006.15.259
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