Julia and John revisited

Nicolae Mihalache. "Julia and John revisited." Fundamenta Mathematicae 215.1 (2011): 67-86. <http://eudml.org/doc/283091>.

@article{NicolaeMihalache2011,
abstract = { We show that the Fatou components of a semi-hyperbolic rational map are John domains. The converse does not hold. This compares to a famous result of Carleson, Jones and Yoccoz for polynomials, in which case the two conditions are equivalent. 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 maps, topological Collet-Eckmann maps and maps satisfying a summability condition (as considered by Graczyk and Smirnov). },
author = {Nicolae Mihalache},
journal = {Fundamenta Mathematicae},
language = {eng},
number = {1},
pages = {67-86},
title = {Julia and John revisited},
url = {http://eudml.org/doc/283091},
volume = {215},
year = {2011},
}

TY - JOUR
AU - Nicolae Mihalache
TI - Julia and John revisited
JO - Fundamenta Mathematicae
PY - 2011
VL - 215
IS - 1
SP - 67
EP - 86
AB - We show that the Fatou components of a semi-hyperbolic rational map are John domains. The converse does not hold. This compares to a famous result of Carleson, Jones and Yoccoz for polynomials, in which case the two conditions are equivalent. 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 maps, topological Collet-Eckmann maps and maps satisfying a summability condition (as considered by Graczyk and Smirnov).
LA - eng
UR - http://eudml.org/doc/283091
ER -