Kolmogorov-Sinai entropy from the ordinal viewpoint

Details Kolmogorov-Sinai entropy from the ordinal viewpoint Kolmogorov-Sinai entropy from the ordinal viewpoint

2009-03-03

arxiv.org/abs/0903.0459v2

Physica D, 239 (2010), pp. 997-1000

Nonlinear Sciences

Chaotic Dynamics

10 pages

Scientific paper

In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. We generally discuss this phenomenon by considering the distribution of ordinal patterns, which describe the up and down in the orbits of a Borel measurable map on a subset of the real numbers. In particular, we give a natural ordinal description of Kolmogorov-Sinai entropy of a large class of one-dimensional dynamical systems and relate Kolmogorov-Sinai entropy to the permutation entropy recently introduced by Bandt and Pompe.

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