V. Penne, Saussol B., Vaienti S.
Dimensions for recurrence times : topological and dynamical properties.
(61K, LATeX 2e)

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.