2008/05/22 by John Taylor, Taylor, John
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.0805.3436
arxiv created 2008/05/22 · arxiv updated 2009/12/01
In this note we consider a collection C of one parameter families of unimodal maps of [0,1]. Each family in the collection has the form uf where u is in [0,1]. Denoting the kneading sequence of uf by K(uf), we will prove that for each member of C, the map u->K(uf) is monotone. It then follows that for each member of C the map u -> h(uf) is monotone, where h(uf) is the topological entropy of uf. For interest, uf(x)=4ux(1-x) and uf(x)=usin(pi x) are shown to belong to C.