| Ritt's theorem and the Heins map in hyperbolic complex manifolds |
| |
| 作者姓名： | Marco Abate Filippo Bracci |
| |
| 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.
|
Ritt's theorem and the Heins map in hyperbolic complex manifolds |
| |
| Marco Abate,Filippo Bracci.Ritt's theorem and the Heins map in hyperbolic complex manifolds[J].Science in China(Mathematics),2005,48(Z1). |
| |
| Authors: | Marco Abate Filippo Bracci |
| |
| Abstract: | 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. |
| |
| Keywords: | holomorphic self-map fixed point Wolff point Ritt's theorem Heins map Stein manifold |
| 本文献已被 万方数据 等数据库收录！ |
