PERIODIC POINTS AND NORMALITY CONCERNING MEROMORPHIC FUNCTIONS WITH MULTIPLICITY  

作　　者：Bingmao DENG Mingliang FANG Yuefei WANG 邓炳茂;方明亮;王跃飞(School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521,China School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521,China;Department of Mathematics,Hangzhou Dianzi University,Hangzhou 310012,China;School of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]School of Financial Mathematics and Statistics,Guangdong University of Finance,Guangzhou 510521,China [2]Department of Mathematics,Hangzhou Dianzi University,Hangzhou 310012,China [3]School of Mathematics and Statistics,Shenzhen University,Shenzhen 518060,China [4]Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Acta Mathematica Scientia》2020年第5期1429-1444,共16页数学物理学报（B辑英文版）

基　　金：supported by the NNSF of China(11901119,11701188);The third author was supported by the NNSF of China(11688101).

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 let ting R(z)be a nonpolynomial 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 let ting F be a family of meromorphic functions in a domain D,and let ting 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.

关 键 词：NORMALITY ITERATION periodic points 

分 类 号：O174.52[理学—数学]