98-547 V. Penne, Saussol B., Vaienti S.
Dimensions for recurrence times : topological and dynamical properties. (61K, LATeX 2e) Aug 2, 98
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Abstract. In this paper we give new properties of the dimension introduced by Afraimovich to characterize Poincar\'e recurrence and that we proposed to call Afraimovich-Pesin's (AP's) dimension. We will show in particular that the 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 sensible to some ``non-generic'' points.

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