Julia and John revisited

• Autorzy: Nicolae Mihalache
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 37F10: Polynomials; rational maps; entire and meromorphic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 215
• Numer: 1
• Strony: 67-86

Daty

wydano

2011

Twórcy

autor

Nicolae Mihalache

• Université Paris Est - Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex France

Identyfikatory

DOI

10.4064/fm215-1-4