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1999, Volume 5, Issue 4: 783-798. Doi: 10.3934/dcds.1999.5.783
This issue Previous Article Homoclinic and multibump solutions for perturbed second order systems using topological degree Next Article Harmonic maps on complete manifolds

Dimensions for recurrence times: topological and dynamical properties

  • 1.

    Centre de Physique Théorique, CNRS Luminy, Case 907, F-13288 Marseille - Cedex 9

  • 2.

    Phymat, Université de Toulon, Centre de Physique Théorique and FRUMAM, Luminy Case 907, 13288 Marseille Cedex 09

Received:  November 30, 1998
Revised:  April 30, 1999
Published:  September 1999
Abstract Related Papers Cited by
    Abstract
  • 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.
    Mathematics Subject Classification: 28D20.

    Citation:
    shu

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