A Solution to the Monotonicity Problem for Unimodal Families
Dynamical Systems
2008-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0805.3436,
title = {A Solution to the Monotonicity Problem for Unimodal Families},
author = {John Taylor},
journal= {arXiv preprint arXiv:0805.3436},
year = {2008}
}