Computing the topological entropy of unimodal maps

Abstract

We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. For this family of maps, the kneading sequence does not determine the lap numbers. The algorithm is obtained by the sign analysis of the itineraries of the critical point and of the boundary points of the interval map. We apply this algorithm to the estimation of the growth number and the topological entropy of maps with direct and reverse bifurcations. © 2012 World Scientific Publishing Company.