On the structure of Fatou domains  

作　　者：CUI GuiZhen PENG WenJuan 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China Mathematics》2008年第7期1167-1186,共20页中国科学：数学（英文版）

基　　金：supported by the National Basic Research Programme of China (Grant No.2006CB805903);the National Natural Science Foundation of China (Grant No.10421101)

摘　　要：Let U be a multiply-connected fixed attracting Fatou domain of a rational map f.We prove that there exist a rational map g and a completely invariant Fatou domain V of g such that(f,U) and(g,V) are holomorphically conjugate,and each non-trivial Julia component of g is a quasi-circle which bounds an eventually superattracting Fatou domain of g containing at most one postcritical point of g.Moreover,g is unique up to a holomorphic conjugation.Let U be a multiply-connected fixed attracting Fatou domain of a rational map f. We prove that there exist a rational map g and a completely invariant Fatou domain V of g such that (f,U) and (g,V) are holomorphically conjugate, and each non-trivial Julia component of g is a quasi-circle which bounds an eventually superattracting Fatou domain of g containing at most one postcritical point of g. Moreover, g is unique up to a holomorphic conjugation.

关 键 词：quasi-conformal surgery PUZZLES quasi-conformally conjugate invariant line fields 37F12 

分 类 号：O177.91[理学—数学]