Dynamics of functions meromorphic outside a small set
Dynamics of functions meromorphic outside a small set
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DOI：
10.1017/s0143385701001328
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发表时间：
2001-06
影响因子：
0.9
通讯作者：
I. N. Baker;P. Domínguez;M. E. Herring
中科院分区：
文献类型：
--
作者：
I. N. Baker;P. Domínguez;M. E. Herring
Fatou和Julia的理论被推广到包括在全不连通紧集E（f）之外的\widehat{\mathbb{C}}中亚纯的函数f的动力学，在E（f）的点处f的簇集是\widehat{\mathbb{C}}。Julia集不仅由标准方法定义，而且还用轨道接近E（f）中一点的点的集合来表征。对于E（f）有OAD类的补且f的逆有有限奇点集的子类，证明了F（f）>中既不存在游荡分支，也不存在Baker域.作为应用，证明了某个一般类的函数具有完全不连通的Julia集.
The theory of Fatou and Julia is extended to include the dynamics of functions f which are meromorphic in \widehat{\mathbb{C}} outside a totally disconnected compact set E(f) at whose points the cluster set of f is \widehat{\mathbb{C}}. The Julia set is defined not only by the standard approach but is also characterized in terms of the set of points whose orbits approach a point of E(f). For the subclass where E(f) has a complement of class OAD and the inverse of f has a finite set of singular points it is shown that neither wandering components nor Baker domains occur in F(f)>. As an application, functions of a certain general class are shown to have a totally disconnected Julia set.