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Julia and John revisited

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Mihalache N.

Fundamenta Mathematicae

2011

tom 215

nr 1

67-86

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).

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Mihalache N.

1 2011

Wyniki wyszukiwania

Julia and John revisited