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

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

2004-11-04

arxiv.org/abs/math/0411086v1

Mathematics

Complex Variables

5 pages; submitted to Proceedings of 2004 Beijing International Conference on Several Complex Variables

Scientific paper

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.

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