[Dimension et mesure pour les applications rationnelles semi-hyperboliques de degré 2]
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.
Accepté le :
Publié le :
Magnus Aspenberg 1 ; Jacek Graczyk 1
@article{CRMATH_2009__347_7-8_395_0, author = {Magnus Aspenberg and Jacek Graczyk}, title = {Dimension and measure for semi-hyperbolic rational maps of degree 2}, journal = {Comptes Rendus. Math\'ematique}, pages = {395--400}, publisher = {Elsevier}, volume = {347}, number = {7-8}, year = {2009}, doi = {10.1016/j.crma.2009.02.016}, language = {en}, }
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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