On the relation of KS entropy and permutation entropy

Since Bandt et al. have shown that the permutation entropy and the Kolmogorov–Sinai entropy coincide for piecewise monotone interval maps, the relationship of both entropies for time-discrete dynamical systems is of a certain interest. The aim of the present paper is a discussion of this relationship on the basis of an ordinal characterization of the Kolmogorov–Sinai entropy recently given.

► Relationship of KS entropy and permutation entropy from the ordinal viewpoint given. ► Open problem of equality of KS entropy and permutation entropy simplified. ► General concept of permutation entropy on the basis of observables given. ► Overview on the state of the art of ordinal description of KS entropy given.