亚纯函数的弱斥性不动点与拟正规族

Weakly Repulsive Fix-Points of Meromorphic Functions and Quasinormal Families

中文关键词:  亚纯函数  弱斥性不动点  拟正规族

英文关键词:meromorphic function  weakly repulsive fixpoint  quasinormal family.

中文摘要:

      本文研究亚纯函数的弱斥性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内最多只有q个弱斥性不动点,则F是D内阶至多为max{4,q+2}的拟正规族。

英文摘要:

      We study the relationship between the weakly repulsive fixpoints of meromorphic functions and quasinormal families. Let F be a family of meromorphic functions in a domain in D and let q≥ 0 be an integer. We obtain that if for each f ∈F there is an integer k = k (f) > 1 such that the k-th iteration f^k of f has q weakly repulsive fixpoints in D , then F is a quasinormal family with order at most max {4,q+ 2} .