超越整函数的某些动力学性质(英文)  

SOME DYNAMICAL PROPERTIES OF TRANSCENDENTAL ENTIRE FUNCTIONS

作　　者：黄志刚[1] 

机构地区：[1]苏州科技学院数理学院,江苏苏州215011

出　　处：《数学杂志》2011年第6期1024-1030,共7页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11001057);NSF of Jiangsu Province(BK2010234);Project of Qinglan of Jiangsu Province

摘　　要：本文研究了由m个超越整函数{f_1,f_2,…,f_m}生成的随机迭代系统的Fatou集分支的某些动力学性质.运用复动力系统理论与双曲度量理论,得到了随机迭代系统有界Fatou分支不存在的一个判别准则,同时回答了Baker所提出的问题,且给出了随机迭代系统Fatou分支为单连通的一个充分条件,推广了Bergweiler的结果.In this paper, we study some dynamical properties of Fatou set of random iteration generated by a family of transcendental entire functions （fl, f2,… , fm）. By using the theory of complex dynamics and hyperbolic metric on hyperbolic domain, we obtain a criterion condition for non-existence of the bounded components of Fatou set. This is an answer to the question raised by Baker. We also give out a sufficient condition for which the Fatou components of random iteration system are simply connected, which is an improvement of Bergweiler＇s result.

关 键 词：有界分支 FATOU集 超越整函数 单连通 

分 类 号：O174.52[理学—数学]