本项目研究一类更广泛的亚纯函数动力系统，也就是在一个完全不连通并且含有无限多个点的紧集之外亚纯的函数。我们主要研究上述函数的Fatou集，拟证明如下两个命题：1. 只有有限个奇异值的上述函数Fatou集没有游荡分支。2.奇异值集有界且其前向轨道与Julia 集的欧式距离为正的上述函数Fatou集没有游荡分支。

In this program we will investigate the dynamics of a class of generalized meromorphic functions which are meromorphic outside a compact totally disconnected set containing infinitely many points. We will mainly study the Fatou set of functions in the above class .and prove the following two propositions: 1. any function in the above class with finitely many singular values has no wandering Fatou component. 2. any function in the above class satisfying that the set of its singular values is bounded and the Euclidean distance between the set of its singular values and its Julia set is positive has no wandering Fatou component.