Kolmogorov-Sinai entropy from recurrence times

M. S. Baptista, E. J. Ngamga, Paulo R. F. Pinto, Margarida Brito, J. Kurths

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


Observing how long a dynamical system takes to return to some state is one of the most simple ways to model and quantify its dynamics from data series. This work proposes two formulas to estimate the KS entropy and a lower bound of it, a sort of Shannon's entropy per unit of time, from the recurrence times of chaotic systems. One formula provides the KS entropy and is more theoretically oriented since one has to measure also the low probable very long returns. The other provides a lower bound for the KS entropy and is more experimentally oriented since one has to measure only the high probable short returns. These formulas are a consequence of the fact that the series of returns do contain the same information of the trajectory that generated it. That suggests that recurrence times might be valuable when making models of complex systems.

Original languageEnglish
Pages (from-to)1135-1140
Number of pages6
JournalPhysics Letters A
Issue number9
Early online date28 Dec 2009
Publication statusPublished - 15 Feb 2010


  • dynamical-systems
  • metric invariant
  • return times
  • statistics
  • complex
  • plots
  • automorphisms
  • signals


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