摘要:本文研究了有理函数复动力系统中 Hermmam 环存在的必要条件，次数大于等于 2 的有理函数 f.若存在 Herman 环 H 则 H 在 ℂ的两个余集分支中至少有两个临界点 (计重数)，并给出存在每个余集分支中恰有两个临界点且临界点落在余集分支的边界的例子。

Abstract:In this paper, we study a necessary condition for the existence of Herman rings in the complex dynamical system of rational functions. If the rational function f of degree greater than or equal to 2 has a Herman ring H, then H has at least two critical points in the two complement components of ℂ. An example is given to show that there are exactly two critical points in each complement component and the critical points are on the boundary.