Permutations and the Kolmogorov-Sinai entropy

Karsten Keller

doi:10.3934/dcds.2012.32.891

Article Contents

2012, Volume 32, Issue 3: 891-900. Doi: 10.3934/dcds.2012.32.891

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Permutations and the Kolmogorov-Sinai entropy

Karsten Keller^1,

1.
Institute of Mathematics, University of Lübeck, Wallstraße 40, D-23560 Luebeck

Received: August 31, 2010

Revised: November 30, 2010

Published: February 2012

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Abstract

This paper provides a way for determining the Kolmogorov-Sinai entropy of time-discrete dynamical systems on the base of quantifying ordinal patterns obtained from a finite set of observables. As a consequence, it is shown that the Kolmogorov-Sinai entropy is bounded from above by a quantity which generalizes the concept of permutation entropy. In this framework, the determination of the Kolmogorov-Sinai entropy of a multidimensional system by use of only a single one-dimensional observable and Takens' embedding theorem is discussed.

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Mathematics Subject Classification: Primary: 28D20; Secondary: 28D05, 37A05.

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References

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