中文摘要：

本文研究了由m个超越整函数{f1，f2，…，fm}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分支不存存的一个判别准则，同时同答了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．

英文摘要：

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.