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Proceedings of the American Mathematical Society

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Iteration of holomorphic maps of the unit ball into itself


Author: Yoshihisa Kubota
Journal: Proc. Amer. Math. Soc. 88 (1983), 476-480
MSC: Primary 32H35; Secondary 30D05, 32A30, 32E35
MathSciNet review: 699417
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Abstract: Let $ \Omega $ be a plane disc and let $ f$ be a holomorphic map of $ \Omega $ into itself. It is known that the iterates $ {f_n}$ of $ f$ converge to a constant $ \zeta \in \bar \Omega $ as $ n \to \infty $ unless $ f$ is a conformal map of $ \Omega $ onto itself. In the present paper it is shown that a more complicated statement of this kind is true in the unit ball of $ {{\mathbf{C}}^N}$.


References [Enhancements On Off] (What's this?)

  • [1] Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
  • [2] Walter Rudin, Function theory in the unit ball of 𝐶ⁿ, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Science], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
  • [3] Georges Valiron, Fonctions analytiques, Presses Universitaires de France, Paris, 1954 (French). MR 0061658

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0699417-X
Keywords: Iteration, holomorphic map, unit ball
Article copyright: © Copyright 1983 American Mathematical Society