N ov 2 00 4 Ritt ’ s theorem and the Heins map in hyperbolic complex manifolds
نویسنده
چکیده
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.
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