# American Institute of Mathematical Sciences

October  1999, 5(4): 783-798. doi: 10.3934/dcds.1999.5.783

## Dimensions for recurrence times: topological and dynamical properties

 1 Centre de Physique Théorique, CNRS Luminy, Case 907, F-13288 Marseille - Cedex 9, France, France 2 Phymat, Université de Toulon, Centre de Physique Théorique and FRUMAM, Luminy Case 907, 13288 Marseille Cedex 09

Received  December 1998 Revised  May 1999 Published  July 1999

In this paper we give new properties of the dimension introduced by Afraimovich to characterize Poincaré recurrence and which we proposed to call Afraimovich-Pesin's (AP's) dimension. We will show in particular that AP's dimension is a topological invariant and that it often coincides with the asymptotic distribution of periodic points : deviations from this behavior could suggest that the AP's dimension is sensitive to some "non-typical" points.
Citation: Vincent Penné, Benoît Saussol, Sandro Vaienti. Dimensions for recurrence times: topological and dynamical properties. Discrete & Continuous Dynamical Systems, 1999, 5 (4) : 783-798. doi: 10.3934/dcds.1999.5.783
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