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.