具有双Herman环的有理函数的拓扑性质

Topological Properties of Rational Functions with Two Herman Rings

摘要: 本文研究了具有两个Herman环的有理函数的拓扑性质。之前的研究中，Wang和Zhang从有理函数的拓扑性质入手，提出了构造具有一个Herman环有理函数的方法，结合周弘毅在2023年的研究，可以得到判断有理函数的拓扑等价类中是否有一个Herman环的充要条件。基于他们的研究，本文进一步给出了具有次数大于或等于2的有理函数拓扑等价于具有两个Herman环的有理函数的必要条件。

Abstract: This paper studies the topological properties of rational functions with two Herman rings. In previous research, Wang and Zhang proposed a method for constructing rational functions with one Herman ring based on the topological properties of rational functions. Combined with Zhou Hongyi’s research in 2023, a necessary and sufficient condition for determining whether there is a Herman ring in the topological equivalence class of rational functions can be obtained. Based on their research, this paper further presents the necessary condition for a rational function with a degree greater than or equal to 2 to be topologically equivalent to a rational function with two Herman rings.