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.
出处
《数学杂志》
CSCD
北大核心
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
关键词
有界分支
FATOU集
超越整函数
单连通
bounded component
Fatou set
transcendental entire function
simply connected
