Density of first Poincare returns, periodic orbits, and Kolmogorov-Sinai entropy

Paulo R. F. Pinto, Murilo S. Baptista, Isabel S. Labouriau

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincare returns. The close relation between periodic orbits and the Poincare returns allows for estimates of relevant quantities in dynamical systems, as the Kolmogorov Sinai entropy, in terms of this density function. Since return times can be trivially observed and measured, our approach to calculate this entropy is highly oriented to the treatment of experimental systems. We also develop a method for the numerical computation of unstable periodic orbits. (C) 2010 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)863-875
Number of pages13
JournalCommunications in Nonlinear Science & Numerical Simulation
Volume16
Issue number2
Early online date25 May 2010
DOIs
Publication statusPublished - Feb 2011

Keywords

  • time returns
  • periodic orbits
  • Lyapunov exponents
  • Kolmogorov entropy
  • recurrence-time statistics
  • chaotic attractors
  • anomalous transport
  • dimensions

Cite this

Density of first Poincare returns, periodic orbits, and Kolmogorov-Sinai entropy. / Pinto, Paulo R. F.; Baptista, Murilo S.; Labouriau, Isabel S.

In: Communications in Nonlinear Science & Numerical Simulation, Vol. 16, No. 2, 02.2011, p. 863-875.

Research output: Contribution to journalArticle

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AB - It is known that unstable periodic orbits of a given map give information about the natural measure of a chaotic attractor. In this work we show how these orbits can be used to calculate the density function of the first Poincare returns. The close relation between periodic orbits and the Poincare returns allows for estimates of relevant quantities in dynamical systems, as the Kolmogorov Sinai entropy, in terms of this density function. Since return times can be trivially observed and measured, our approach to calculate this entropy is highly oriented to the treatment of experimental systems. We also develop a method for the numerical computation of unstable periodic orbits. (C) 2010 Elsevier B.V. All rights reserved.

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KW - Lyapunov exponents

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KW - recurrence-time statistics

KW - chaotic attractors

KW - anomalous transport

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