Holomorphic maps from 𝐶ⁿ to 𝐶ⁿ

Rosay, Jean-Pierre; Rudin, Walter

doi:10.1090/S0002-9947-1988-0929658-4

Holomorphic maps from $\textbf {C}^ n$ to $\textbf {C}^ n$
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by Jean-Pierre Rosay and Walter Rudin PDF

Trans. Amer. Math. Soc. 310 (1988), 47-86 Request permission

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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