  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.
