关于随机动力系统的Fatou－Julia猜测

ON THE FATOU AND JULIA CONJECTURE FOR THE RANDOM DYNAMICAL SYSTEM

设Ｆ＝｛ｆ１，…，ｆＭ｝是一个次数大于１的多项式集合。我们证明了在一定条件下Ｆａｔｏｕ集Ｆ（Ｆ）没有游荡区域。更确切地说，对于Ｆ（Ｆ）的每一个分支Ω，存在整数ｍ≥０，ｎ≥０。

Let F={f 1,…,f M} be a set of polynomials with degree more than one. We prove that the Fatou set F(F) has no wandering domains under some conditions. More precisely, for every component Ω of F(F) , there exist integers m≥0,n≥0,m≠n and a σ∈∑ M such that W m σ(Ω) and W n σ(Ω) stay in the same component of F(F ).