Ritt’s theorem and the Heins map in hyperbolic complex manifolds |
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Authors: | Marco Abate Filippo Bracci |
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Affiliation: | 1.Dipartimento di Matematica,Università di Pisa,Italy;2.Dipartimento di Matematica,Università di Roma “Tor Vergata201D, Via della Ricerca Scientifica,Roma,Italy |
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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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