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 tau(f) is an element of X, which is attracting. Furthermore, we shall prove that tau(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.
|Autori:||Abate M; Bracci F|
|Titolo:||Ritt's theorem and the Heins map in hyperbolic complex manifolds|
|Anno del prodotto:||2005|
|Digital Object Identifier (DOI):||10.1360/05za0017|
|Appare nelle tipologie:||1.1 Articolo in rivista|