Julia and John revisited
Dynamical Systems
2009-02-26 v3
Abstract
We show that Fatou components of a semi-hyperbolic rational map are John domains and that the converse does not hold. This generalizes a famous result of Carleson, Jones and Yoccoz. We show that a connected Julia set is locally connected for a large class of non-uniformly hyperbolic rational maps. This class is more general than semi-hyperbolicity and includes Collet-Eckmann and Topological Collet-Eckmann maps and maps verifying a summability condition (as considered by Graczyk and Smirnov).
Keywords
Cite
@article{arxiv.0803.3889,
title = {Julia and John revisited},
author = {Nicolae Mihalache},
journal= {arXiv preprint arXiv:0803.3889},
year = {2009}
}