Resonances and Constructions of Fatou-Bieberbach Maps

We study and analyze a proof of a theorem by Rosay and Rudin on the Fatou-Bieberbach method of constructing biholomorphic images of Cn in Cn, starting with an automorphism with an attracting xed point. We thoroughly investigate constructions of Fatou- Bieberbach maps. As a result, we lay much emphasis on the concept of resonances and how they aect our attempt to linearize an automorphism with an attracting xed point, by a biholomorphic change of variables. We give several examples and some basic explanations to several concepts in order to give an in-depth and basic feel of the whole proof