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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699417-X
PII: S 0002-9939(1983)0699417-X
Keywords: Iteration, holomorphic map, unit ball
Article copyright: © Copyright 1983 American Mathematical Society