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Comptes Rendus Mathématique
Volume 353, n° 8
pages 701-704 (août 2015)
Doi : 10.1016/j.crma.2015.05.001
Received : 19 Mars 2015 ;  accepted : 19 May 2015
Brody curves in complicated sets
Courbes de Brody dans quelques ensembles compliqués
 

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

Abstract

For a hyperbolic generalized Hénon mapping (in the sense of [[3]]),  , 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   (see [[3], [6]]). We prove that there exists a leaf, which is an injective Brody curve in  , in the lamination of   for certain generalized Hénon mappings (for Brody curves and injective Brody curves, see Subsection 2.2).

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Résumé

L'ensemble   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   (voir [[3], [6]]). Nous montrons que, pour certaines applications de Hénon généralisées hyperboliques, une feuille de cette lamination   est une courbe de Brody injective dans   (voir la sous-section 2.2 pour les notions de courbes de Brody et courbes de Brody injectives).

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