Dynamics of regularly ramified rational maps. I: Julia sets of maps in one-parameter families
A holomorphic or meromorphic function which is invariant under the group of linear transformations is called an automorphic function. This paper mainly considers the dynamics of rational automorphic functions, which are called regularly ramified rational maps. There are five kinds of such groups: the cyclic group \(G_1\), the dihedral group \(G_2\), the tetrahedral group \(G_3\), the octahedral group \(G_4\) and icosahedral group \(G_5\). The dynamics of rational maps invariant under \(G_1\) and its moduli spaces has been investigated by \textit{J. Milnor} in [Exp. Math. 9, No. 4, 481--522 (2000; Zbl 0972.30013)]. This paper mainly explores the Julia sets of rational maps invariant under the other four groups. Many interesting examples are presented.
scientific article; zbMATH DE number 6919374
scientific article