Density of first Poincaré returns, periodic orbits, and Kolmogorov–Sinai entropy

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10 Citations (Scopus)


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 Poincaré returns. The close relation between periodic orbits and the Poincaré 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.

Original languageEnglish
Pages (from-to)863 -875
Number of pages14
JournalCommunications in Nonlinear Science & Numerical Simulation
Issue number2
Early online date25 May 2010
Publication statusPublished - Feb 2011


  • Time returns
  • Periodic orbits
  • Lyapunov exponents
  • Kolmogorov entropy


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