Resonances and Constructions of Fatou-Bieberbach Maps
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We study and analyze a proof of a theorem by Rosay and Rudin on the Fatou-Bieberbachmethod of constructing biholomorphic images of Cn in Cn, starting with an automorphismwith an attracting xed point. We thoroughly investigate constructions of Fatou-Bieberbach maps. As a result, we lay much emphasis on the concept of resonances andhow 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 explanationsto several concepts in order to give an in-depth and basic feel of the wholeproof.