Brody curves in complicated sets

Ahn, Taeyong

doi:10.1016/j.crma.2015.05.001

Complex analysis/Dynamical systems

Brody curves in complicated sets
[Courbes de Brody dans quelques ensembles compliqués]

Présenté par : Jean-Pierre Demailly

Ahn, Taeyong ¹

¹ Center for Geometry and its Applications, POSTECH, Pohang 790-784, Republic of Korea

Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 701-704.

Résumé
Abstract

L'ensemble $J^{+}$ des points d'orbite bornée est connu, pour une application de Hénon généralisée hyperbolique (dans le sens de [3]), comme étant un ensemble compliqué admettant une lamination par images biholomorphes de $C$ (voir [3,6]). Nous montrons que, pour certaines applications de Hénon généralisées hyperboliques, une feuille de cette lamination $J^{+}$ est une courbe de Brody injective dans $P^{2}$ (voir la sous-section 2.2 pour les notions de courbes de Brody et courbes de Brody injectives).

For a hyperbolic generalized Hénon mapping (in the sense of [3]), $J^{+}$ , the boundary of the set of points with bounded orbit is known as a complicated set and also known to admit a lamination by biholomorphic images of $C$ (see [3,6]). We prove that there exists a leaf, which is an injective Brody curve in $P^{2}$ , in the lamination of $J^{+}$ for certain generalized Hénon mappings (for Brody curves and injective Brody curves, see Subsection 2.2).

Reçu le : 2015-03-19
Accepté le : 2015-05-19
Publié le : 2015-06-19

DOI : 10.1016/j.crma.2015.05.001

Affiliations des auteurs :

Ahn, Taeyong ¹

¹ Center for Geometry and its Applications, POSTECH, Pohang 790-784, Republic of Korea

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     title = {Brody curves in complicated sets},
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Ahn, Taeyong. Brody curves in complicated sets. Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 701-704. doi : 10.1016/j.crma.2015.05.001. http://www.numdam.org/articles/10.1016/j.crma.2015.05.001/

Bibliographie
Cité par

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[6] Fornæss, J.E.; Sibony, N. Complex Hénon mappings in $C^{2}$ and Fatou–Bieberbach domains, Duke Math. J., Volume 65 (1992), pp. 345-380

[7] Hubbard, J.H.; Oberste-Vorth, R. Hénon mappings in the complex domain I: the global topology of dynamical space, Publ. Math. Inst. Hautes Études Sci., Volume 79 (1994), pp. 5-46

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[9] Sibony, N. Dynamique des applications rationnelles de $P^{k}$ , Panor. Synth., Volume 8 (1999), pp. 97-185

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