| On the structure of Fatou domains |
| |
| 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.
|
On the structure of Fatou domains |
| |
| Authors: | GuiZhen Cui WenJuan Peng |
| |
| Institution: | 1.Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing,China |
| |
| Abstract: | 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. |
| |
| Keywords: | quasi-conformal surgery puzzles quasi-conformally conjugate invariant line fields |
| 本文献已被 SpringerLink 等数据库收录！ |
