A Wong-Rosay type theorem for proper holomorphic self-maps

Opshtein, Emmanuel

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 19 (2010) no. 3-4, pp. 513-524.

Dans cette note, nous prouvons que les seules auto-applications holomorphes propres des domaines bornés de ${ℂ}^k$ dont les itérées accumulent un point de stricte-pseudoconvexité du bord sont des automorphismes de la boule. Il s’agit d’un résultat de type Wong-Rosay pour une suite d’applications dont les degrés sont à priori non bornés.

In this short paper, we show that the only proper holomorphic self-maps of bounded domains in ${ℂ}^k$ whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are a priori unbounded.

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