论文信息 - Dimensions for recurrence times: topological and dynamical properties

Dimensions for recurrence times: topological and dynamical properties

In this paper we give new properties of the dimension introduced by Afraimovich to characterize Poincare 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.

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