no. 7-8
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

Aspenberg, Magnus1 ; Graczyk, Jacek1
1 Laboratoire de mathématique, Université de Paris-Sud, 91405 Orsay cedex, France
Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 395-400.

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2009.02.016
Aspenberg, Magnus 1 ; Graczyk, Jacek 1

1 Laboratoire de mathématique, Université de Paris-Sud, 91405 Orsay cedex, France 
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Aspenberg, Magnus; Graczyk, Jacek. Dimension and measure for semi-hyperbolic rational maps of degree 2. Comptes Rendus. Mathématique, Tome 347 (2009) no. 7-8, pp. 395-400. doi : 10.1016/j.crma.2009.02.016. http://archive.numdam.org/articles/10.1016/j.crma.2009.02.016/

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