The maximal entropy measure detects non-uniform hyperbolicity
Dynamical Systems
2010-05-18 v1 Complex Variables
Abstract
We characterize two of the most studied non-uniform hyperbolicity conditions for rational maps, semi-hyperbolicity and the topological Collet-Eckmann condition, in terms of the maximal entropy measure. Using the same tools in the proof of these results we give an extension of a result of Carleson, Jones and Yoccoz, that semi-hyperbolicity characterizes those polynomial maps whose basin of attraction of infinity is a John domain, to rational maps having a completely invariant attracting basin.
Cite
@article{arxiv.1005.2640,
title = {The maximal entropy measure detects non-uniform hyperbolicity},
author = {Juan Rivera-Letelier},
journal= {arXiv preprint arXiv:1005.2640},
year = {2010}
}
Comments
Comments welcomed