Geodesic
Julia and John revisited
Nicolae Mihalache1
1 Université Paris Est – Créteil 61 avenue du Général de Gaulle 94010 Créteil Cedex France
Fundamenta Mathematicae, Tome 215 (2011) no. 1, pp. 67-86

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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).
DOI : 10.4064/fm215-1-4
Keywords: fatou components semi hyperbolic rational map john domains converse does compares famous result carleson jones yoccoz polynomials which conditions equivalent connected julia set locally connected large class non uniformly hyperbolic rational maps class general semi hyperbolicity includes collet eckmann maps topological collet eckmann maps maps satisfying summability condition considered graczyk smirnov

Nicolae Mihalache 1

1 Université Paris Est – Créteil 61 avenue du Général de Gaulle 94010 Créteil Cedex France 
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Nicolae Mihalache. Julia and John revisited. Fundamenta Mathematicae, Tome 215 (2011) no. 1, pp. 67-86. doi: 10.4064/fm215-1-4

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