Comptes Rendus
no. 8
Complex analysis/Dynamical systems
Brody curves in complicated sets
[Courbes de Brody dans quelques ensembles compliqués]

Présenté par : Jean-Pierre Demailly

Taeyong Ahn1
1 Center for Geometry and its Applications, POSTECH, Pohang 790-784, Republic of Korea
Comptes Rendus. Mathématique, Volume 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
Taeyong Ahn 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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Taeyong Ahn. Brody curves in complicated sets. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 701-704. doi : 10.1016/j.crma.2015.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2015.05.001/

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

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

[3] E. Bedford; J. Smillie Polynomial diffeomorphisms of C2: currents, equilibrium measure and hyperbolicity, Invent. Math., Volume 103 (1991) no. 1, pp. 69-99

[4] E. Bedford; M. Lyubich; J. Smillie Polynomial diffeomorphisms of C2: IV. The measure of maximal entropy and laminar currents, Invent. Math., Volume 112 (1993) no. 1, pp. 77-125

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

[6] J.E. Fornæss; N. Sibony Complex Hénon mappings in C2 and Fatou–Bieberbach domains, Duke Math. J., Volume 65 (1992), pp. 345-380

[7] J.H. Hubbard; R. Oberste-Vorth 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] M. Shub Global Stability of Dynamical Systems, Springer-Verlag, 1987

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

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