Dimension and measure for semi-hyperbolic rational maps of degree 2

Magnus Aspenberg; Jacek Graczyk

doi:10.1016/j.crma.2009.02.016

Dynamical Systems

Dimension and measure for semi-hyperbolic rational maps of degree 2
[Dimension et mesure pour les applications rationnelles semi-hyperboliques de degré 2]

Présenté par : Étienne Ghys

Magnus Aspenberg ¹ ; Jacek Graczyk ¹

¹ Laboratoire de mathématique, Université de Paris-Sud, 91405 Orsay cedex, France

Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 395-400.

Résumé
Abstract

Nous démontrons que presque toute application rationnelle semi-hyperbolique de degré 2 a au moins un point critique récurrent. Cette estimation est optimale parce que l'ensemble des applications rationnelles avec tous les points critiques non-récurrents est de pleine dimension de Hausdorff.

We prove that almost every non-hyperbolic rational map of degree 2 has at least one recurrent critical point. This estimate is optimal because the set of rational maps with all critical points non-recurrent is of full Hausdorff dimension.

Reçu le : 2008-05-27
Accepté le : 2009-02-11
Publié le : 2009-03-17

DOI : 10.1016/j.crma.2009.02.016

Affiliations des auteurs :

Magnus Aspenberg ¹ ; Jacek Graczyk ¹

¹ Laboratoire de mathématique, Université de Paris-Sud, 91405 Orsay cedex, France

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     title = {Dimension and measure for semi-hyperbolic rational maps of degree 2},
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     doi = {10.1016/j.crma.2009.02.016},
     language = {en},
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Magnus Aspenberg; Jacek Graczyk. Dimension and measure for semi-hyperbolic rational maps of degree 2. Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 395-400. doi : 10.1016/j.crma.2009.02.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.016/

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