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Ritt's theorem and the Heins map in hyperbolic complex manifolds | | Marco Abate
; Filippo Bracci
; | | Date: |
4 Nov 2004 | | Subject: | Complex Variables; Dynamical Systems MSC-class: 32H50 (Primary); 32Q45, 37F99 (Secondary) | math.CV math.DS | | 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 of X such that f(X) is relatively compact in X has a unique fixed point p(f) in X, which is attracting. Furthermore, we shall prove that p(f) depends holomorphically on f in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author. | | Source: | arXiv, math.CV/0411086 | | Services: | Forum | Review | PDF | Favorites | |
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