Computing the topological entropy of unimodal maps

2010/12/09 by Rui Dilão, Dilão, Rui, José Amigó +1
Mathematics · Physics and Astronomy · #37B10 #37B40 #37E05 #37G35 #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #math.DS #msc:37B10 #msc:37B40 #msc:37E05 #msc:37G35 #nlin.CD

paper · pdf · doi:10.48550/arxiv.1012.1997

25 pages, 3 figures

arxiv created 2010/12/09 · arxiv updated 2016/08/14

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. 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.

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