Ritt's theorem and the Heins map in hyperbolic complex manifolds

作     者：Marco Abate Filippo Bracci 

作者机构：Dipartimento di Matematica Università di PisaLargo Pontecorvo 556127 PisaItalyDipartimento di Matematica Università di Roma "Tor Vergata"Via della Ricerca Scientifica00133 RomaItaly 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2005年第48卷第Z1期

页      面：238-243页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Ministero dell’Istruzione  dell’Università e della Ricerca  MIUR 

主　　题：holomorphic self-map, fixed point, Wolff point, Ritt's theorem, Heins map, Stein manifold. 

摘      要：Let X be a Kobayashi hyperbolic complex manifold, and assume that X does not contain compact complex submanifolds of positive dimension (e.g., X Stein). We shall prove the following generalization of Ritt s theorem: every holomorphic self-map f: X →X such that f(X) is relatively compact in X has a unique fixed point τ(f) ∈ X, which is attracting. Furthermore, we shall prove that τ(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.