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Journal of Statistical Physics

, Volume 106, Issue 3–4, pp 623–634 | Cite as

Recurrence, Dimensions, and Lyapunov Exponents

  • B. Saussol
  • S. Troubetzkoy
  • S. Vaienti
Article

Abstract

We show that the Poincaré return time of a typical cylinder is at least its length. For one dimensional maps we express the Lyapunov exponent and dimension via return times.

return time 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • B. Saussol
    • 1
  • S. Troubetzkoy
    • 2
  • S. Vaienti
    • 3
  1. 1.LAMFA/CNRS fre 2270Université de Picardie Jules VerneAmiens Cedex 1France
  2. 2.Institut de Mathématiques de Luminy et Federation de Recherches des Unites de Mathematique de MarseilleCentre de Physique ThéoriqueMarseille Cedex 9France
  3. 3.Centre de Physique Théorique et Federation de Recherches des Unites de Mathematique de MarseillePhymat, Université de Toulon et du VarMarseille Cedex 9France

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