PERIODIC POINTS AND NORMALITY CONCERNING MEROMORPHIC FUNCTIONS WITH MULTIPLICITY

• 作者: Bingmao DENG Mingliang FANG Yuefei WANG
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2020,（5）
• 页码范围: 1429-1444
• 页数: 16页
• 语种: 英文

摘要

In this article,two results concerning the periodic points and normality of meromorphic functions are obtained: (i) the exact lower bound for the numbers of periodic points of rational functions with multiple fixed points and zeros is proven by letting R(z) be a non-polynomial rational function,and if all zeros and poles of R(z)-z are multiple,then Rk(z)has at least k + 1 fixed points in the complex plane for each integer k ≥ 2;(ii) a complete solution to the problem of normality of meromorphic functions with periodic points is given by letting F be a family of meromorphic functions in a domain D,and letting k ≥ 2 be a positive integer.If,for each f ∈ F,all zeros and poles of f(z)-z are multiple,and its iteration fk has at most k distinct fixed points in D,then F is normal in D.Examples show that all of the conditions are the best possible.