Comptes Rendus
Dynamical Systems
Dimension and measure for semi-hyperbolic rational maps of degree 2
Comptes Rendus. Mathématique, Volume 347 (2009) no. 7-8, pp. 395-400.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.02.016
Magnus Aspenberg 1; Jacek Graczyk 1

1 Laboratoire de mathématique, Université de Paris-Sud, 91405 Orsay cedex, France
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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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[5] C.T. McMullen Complex Dynamics and Renormalization, Annals of Mathematics Studies, vol. 135, Princeton Univ. Press, Princeton, NJ, 1994 (x+214)

[6] R. Mañé On a theorem of Fatou, Bol. Soc. Brasil. Mat. (N.S.), Volume 24 (1993), pp. 1-11

[7] R. Mañé; P. Sad; D. Sullivan On the dynamics of rational maps, Ann. Sci. École Norm. Sup., Volume 16 (1983), pp. 193-217

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