Monotonicity of entropy for real multimodal maps
Dynamical Systems
2013-12-11 v2
Abstract
In \cite{Mil}, Milnor posed the {\em Monotonicity Conjecture} that the set of parameters within a family of real multimodal polynomial interval maps, for which the topological entropy is constant, is connected. This conjecture was proved for quadratic by Milnor & Thurston \cite{MT} and for cubic maps by Milnor & Tresser, see \cite{MTr} and also \cite{DGMT}. In this paper we will prove the general case.
Cite
@article{arxiv.0905.3377,
title = {Monotonicity of entropy for real multimodal maps},
author = {Henk Bruin and Sebastian van Strien},
journal= {arXiv preprint arXiv:0905.3377},
year = {2013}
}
Comments
Final version. To appear in Journal of the AMS