Kolmogorov-Sinai entropy from the ordinal viewpoint

Abstract

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.

10 pages

References in corpus (1)

• The permutation entropy rate equals the metric entropy rate for ergodic information sources and ergodic dynamical systems

Cited by in corpus (13)

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• Permutation Excess Entropy and Mutual Information between the Past and Future
• Ordinal Pattern Dependence in the Context of Long-Range Dependence
• Complexity-based permutation entropies: from deterministic time series to white noise
• Differential symbolic entropy in nonlinear dynamics complexity analysis