Journal of Statistical Physics

, Volume 86, Issue 1–2, pp 191–212 | Cite as

Recurrence time statistics in chaotic dynamics. I. Discrete time maps

  • V. Balakrishnan
  • G. Nicolis
  • C. Nicolis
Articles

Abstract

The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markow maps the recurrence problem is cast into a-renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values.

Key Words

Recurrence time escape time Markov partition fully developed chaos intermittent chaos 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • V. Balakrishnan
    • 1
    • 2
  • G. Nicolis
    • 2
  • C. Nicolis
    • 3
  1. 1.Department of PhysicsIndian Institute of TechnologyMadrasIndia
  2. 2.Center for Nonlinear Phenomena and Complex SystemsUniversité Libre de BruxellesBrusselsBelgium
  3. 3.Institut Royal Météorologique de BelgiqueBrusselsBelgium

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