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Holomorphic maps from \(C^ n\) to \(C^ n\). (English) Zbl 0708.58003
Summary: We study holomorphic mappings from \({\mathbb{C}}^ n\) to \({\mathbb{C}}^ n\), 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 \({\mathbb{C}}^ n\) is finite. An Appendix is devoted to the question of linearization of contractions.

MSC:
58C10 Holomorphic maps on manifolds
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
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