亚纯函数的不动点与拟正规族

Fixpoints of Mermorphic Functions and Quasinormal Families

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.