论文标题
Meromormormormorphic功能的FATOU组件的连通性
Connectivity of Fatou Components of Meromorphic Functions
论文作者
论文摘要
在本文中，我们表明存在具有2个周期的FATOU组件的循环，其中一个简单地连接，另一个是双重连接的。特别是，双重连接的FATOU组件可以是吸引人，抛物线或贝克域。因此，这解决了一个问题，即双重连接的周期性FATOU组件是否必须是Herman戒指。 我们还证明存在具有最终连接性的流浪域的先验性异常功能。此外，我们表明该徘徊域的连接序列与第二周期是周期性的。这解决了关于流浪域的最终连接性不存在的问题，并给出了Ferreira构建的不同示例[J.伦敦数学。 Soc。 （2022），doi：10.1112/jlms.12613]。
In this paper, we show that there exist transcendental meromorphic functions with a cycle of 2-periodic Fatou components, where one is simply connected while the other is doubly connected. In particular, the doubly connected Fatou component can be an attracting, parabolic, or Baker domain. Thus, this settles the problem of whether a doubly connected periodic Fatou component must be a Herman ring. We also prove that there exists a transcendental meromorphic function with a wandering domain that has no eventual connectivity. In addition, we show that the connectivity sequence of this wandering domain is periodic with period two. This solves a problem about the nonexistence of the eventual connectivity of wandering domains and gives a different example constructed by Ferreira [J. London Math. Soc. (2022), DOI:10.1112/jlms.12613].
