Ergodicity from the ordinal viewpoint
نویسندگان
چکیده
In the case of ergodicity much of the structure of a one-dimensional time-discrete dynamical system is already determined by its ordinal structure. In order to explain this phenomenon more precisely, we show that ordinal patterns, which describe the up and down in the orbits of an ergodic Borel measurable map on a subset of the real numbers, are in a certain sense generating. On this base we give statements relating Kolmogorov-Sinai entropy to the permutation entropy recently introduced by Bandt and Pompe.
منابع مشابه
Kolmogorov-Sinai entropy from the ordinal viewpoint
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...
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