随机迭代系统的有界Fatou分支的存在性

摘要

本文研究了由m个超越整函数函数f1,f2,…,fm生成的随机迭代系统的Fatou分支的有界性问题.利用复动力系统理论的方法,得到一个Fatou连通分支U分别作为游荡域和非游荡域有界的条件,推广了Zheng的结果,同时也是对Baker的问题在随机迭代系统情形的一个回答.%In this article, we study the boundedness of components of Fatou set of random iteration generated by the family {f1, f2,…,fm}. By using the theory of complex dynamcis, some conditions are given for which the wandering component and non-wandering component of Fatou set are bounded. This is an extension of Zheng's result, and it is also an answer to the question raised by Baker.