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Recurrence time statistics for finite size intervals.

Eduardo G Altmann1, Elton C da Silva, Ibere L Caldas

  • 1Instituto de Física, Universidade de São Paulo, C.P. 66318, 05315-970 São Paulo, São Paulo, Brazil. altmann@if.usp.br

Chaos (Woodbury, N.Y.)
|December 1, 2004
PubMed
Summary
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Recurrence statistics in chaotic systems typically show exponential decay, but short-term memory effects from unstable orbits alter this pattern. Careful interval selection is crucial for accurate Poincare recurrence time analysis.

Area of Science:

  • Physics
  • Mathematics
  • Dynamical Systems

Background:

  • Chaotic dynamical systems exhibit complex behaviors.
  • Understanding recurrence times is key to characterizing system dynamics.

Purpose of the Study:

  • Investigate recurrence statistics in finite-sized intervals for chaotic systems.
  • Analyze the impact of short-term memory effects on recurrence distributions.

Main Methods:

  • Statistical analysis of recurrence times.
  • Theoretical interpretation linked to unstable periodic orbits.

Main Results:

  • Typical exponential decay in recurrence times, with deviations at short times due to memory effects.
  • Memory effects are attributed to unstable periodic orbits within the interval.

Related Experiment Videos

  • Exponential decay converges to Poissonian statistics as interval width approaches zero for strongly mixing systems.

    • Conclusions:

    • Short-term memory effects, though localized, significantly influence overall recurrence distributions.
    • Attention to interval size is critical for accurate numerical and experimental Poincare recurrence time calculations.