亚纯函数的不动点与拟正规族  

Fixpoints of Mermorphic Functions and Quasinormal Families

作　　者：王淑贵[1] 伍胜健[2] 

机构地区：[1]新疆石河子大学数学系,新疆石河子832000 [2]北京大学数学科学学院,北京100871

出　　处：《数学学报（中文版）》2002年第3期545-550,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(19871002)

摘　　要：本文研究了亚纯函数的不动点与拟正规族的关系，得到了以下结果：设F 是区域Ｄ内的亚纯函数族，ｑ是一个非负整数．如果对任意的ｆ∈Ｆ存在自然数ｋ＝ｋ（ｆ）＞１使得ｆ的 ｋ次迭代ｆ～ｋ在 Ｄ内最多有 ｑ个不动点，则Ｆ是 Ｄ内阶至多为ｍａｘ｛４，ｑ＋３｝的拟正规族．This paper studies the relationship between fixpoints of meromorphic func- tions and quasinormal families and the following results are obtained. Let F be a family of meromorphic functions in domain D and let q be a nonnegative integer. If for every f∈F there is a positive integer k = k(f) > 1 such that the k-th iteration jk of f has at most q fixpoints in D, then F is a quasinormal family with order at most max{4, q + 3} in D.

关 键 词：亚纯函数 不动点 拟正规族 

分 类 号：O174.52[理学—数学]