Permutations and topological entropy for interval maps

Abstract

Recently Bandt, Keller and Pompe (2002 Entropy of interval maps via permutations Nonlinearity 15 1595–602) introduced a method of computing the entropy of piecewise monotone interval maps by counting permutations exhibited by initial pieces of orbits. We show that for topological entropy this method does not work for arbitrary continuous interval maps. We also show that for piecewise monotone interval maps topological entropy can be computed by counting permutations exhibited by periodic orbits.