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Julia and John revisited

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).
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https://hal-upec-upem.archives-ouvertes.fr/hal-00796882
Contributor : Nicolae Mihalache <>
Submitted on : Tuesday, March 5, 2013 - 11:17:28 AM
Last modification on : Thursday, March 19, 2020 - 12:26:02 PM

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Nicolae Mihalache. Julia and John revisited. Fundamenta Mathematicae, Instytut Matematyczny, Polskiej Akademii Nauk,, 2011, 215 (1), pp.67-86. ⟨10.4064/fm215-1-4⟩. ⟨hal-00796882⟩

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