Iteration of holomorphic maps of the unit ball into itself
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- by Yoshihisa Kubota PDF
- Proc. Amer. Math. Soc. 88 (1983), 476-480 Request permission
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
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
- Georges Valiron, Fonctions analytiques, Presses Universitaires de France, Paris, 1954 (French). MR 0061658
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 476-480
- MSC: Primary 32H35; Secondary 30D05, 32A30, 32E35
- DOI: https://doi.org/10.1090/S0002-9939-1983-0699417-X
- MathSciNet review: 699417