Holomorphic maps from 𝐶ⁿ to 𝐶ⁿ

Source abstract

We study holomorphic mappings from C n {{\mathbf {C}}^n} to C n {{\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 C n {{\mathbf {C}}^n} is finite. An Appendix is devoted to the question of linearization of contractions.