Holomorphic maps from \(C^ n\) to \(C^ n\). (English) Zbl 0708.58003

Rosay, Jean-Pierre; Rudin, Walter

Trans. Am. Math. Soc. 310, No. 1, 47-86 (1988).

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

Keywords:

holomorphic mapping on countable sets; holomorphic mappings from \({\mathbb{C}}^ n\) to \({\mathbb{C}}^ n\); Fatou-Bieberbach maps