Complex analysis/Dynamical systems
Brody curves in complicated sets
[Courbes de Brody dans quelques ensembles compliqués]
Comptes Rendus. Mathématique, Tome 353 (2015) no. 8, pp. 701-704.

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 P2 (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 P2, in the lamination of J+ for certain generalized Hénon mappings (for Brody curves and injective Brody curves, see Subsection 2.2).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2015.05.001
Ahn, Taeyong 1

1 Center for Geometry and its Applications, POSTECH, Pohang 790-784, Republic of Korea
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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://archive.numdam.org/articles/10.1016/j.crma.2015.05.001/

[1] Ahn, T. Foliation structure for generalized Hénon mappings, University of Michigan, USA, 2012 (PhD thesis)

[2] Ahn, T. Foliation structure for generalized Hénon mappings (preprint) | arXiv

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[5] Brody, R. Compact manifolds and hyperbolicity, Trans. Amer. Math. Soc., Volume 235 (1978), pp. 213-219

[6] Fornæss, J.E.; Sibony, N. Complex Hénon mappings in C2 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

[8] Shub, M. Global Stability of Dynamical Systems, Springer-Verlag, 1987

[9] Sibony, N. Dynamique des applications rationnelles de Pk, Panor. Synth., Volume 8 (1999), pp. 97-185

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