Zalcman引理在随机迭代函数族动力系统中的应用  

An Application of Zalcman Lemma in Dynamical Systems of Random Iterated Function Families

作　　者：黄小杰[1,2] 刘芝秀 Xiao Jie HUANG;Zhi Xiu LIU(Department of Science,Nanchang Institute of Technology,Jiangxi 330099,P.R.China;School of Computer Science and Technology,Fudan University,Shanghai 200433,P.R.China)

机构地区：[1]南昌工程学院理学院,江西330099 [2]复旦大学计算机科学技术学院,上海200433

出　　处：《数学学报（中文版）》2020年第5期531-536,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11671091,11731003);江西省教育厅科技项目(GJJ180944,GJJ190963)。

摘　　要：本文根据Schwick的思想,利用Zalcman引理讨论了随机迭代函数族动力系统,指出了函数族随机迭代动力系统的Fatou集和函数族衍生半群动力系统的Fatou集定义差别明显但却等价.并获得了如下正规定则,设F={fi|fi为C(C)上的非线性解析函数,i∈M},其中M为非空指标集,ΣM={(j1,j2,…,jn,…)|ji∈M,i∈N},若对任意的指标序列σ=(j1,j2,…,jn,…)∈ΣM,迭代序列{Wσn=fjn■fjn-1■…■fj1(z)|n∈N}在点z处正规,则函数族F本身在点z处正规.In this paper,it studies the properties of dynamical systems about random iterated of function family based on the idea of Schwick and using the Zalcman lemma.It points out that the Fatou set's definition of random dynamics and the Fatou set's definitions of dynamics of semigroups of a function family are obviously different but equivalent.Furthermore,the following normal criterion is obtained.Let F={fi|fi is a nonlinear analytic function on C(C),i∈M},where M is non empty index set,ΣM={(j1,j2,…,jn,…)|ji∈M,i∈N},if for any index sequenceσ=(j1,j2,…,jn,…)∈ΣM,the iterative sequence{Wσn=fjn■fjn-1■…■fj1(z)|n∈N}is normal at point z,then the function family F is also normal at point z.

关 键 词：随机动力系统 半群动力系统 JULIA集 排斥周期点 正规族 

分 类 号：O174.5[理学—数学]