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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Holomorphic maps from $ {\bf C}\sp n$ to $ {\bf C}\sp n$


Authors: Jean-Pierre Rosay and Walter Rudin
Journal: Trans. Amer. Math. Soc. 310 (1988), 47-86
MSC: Primary 32H35
MathSciNet review: 929658
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Abstract: We study holomorphic mappings from $ {{\mathbf{C}}^n}$ to $ {{\mathbf{C}}^n}$, and especially their action on countable sets. Several classes of countable sets are considered. Some new examples of Fatou-Bieberbach maps are given, and a nondegenerate map is constructed so that the volume of the image of $ {{\mathbf{C}}^n}$ is finite. An Appendix is devoted to the question of linearization of contractions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0929658-4
PII: S 0002-9947(1988)0929658-4
Keywords: Immersion-interpolation, tame sets, unavoidable sets, rigid sets, shears, Fatou-Bieberbach regions
Article copyright: © Copyright 1988 American Mathematical Society