On connectivity of Fatou components concerning a family of rational maps
Summary: I. N. Baker established the existence of Fatou component with any given finite connectivity by the method of quasi-conformal surgery. M. Shishikura suggested giving an explicit rational map which has a Fatou component with finite connectivity greater than 2. In this paper, considering a family of rational maps \(R \left(z, t\right)\) that A. F. Beardon proposed, we prove that \(R \left(z, t\right)\) has Fatou components with connectivities 3 and 5 for any \(t \in \left(0, \left.1 / 12\right]\right.\). Furthermore, there exists \(t \in \left(0, \left.1 / 12\right]\right.\) such that \(R \left(z, t\right)\) has Fatou components with connectivity nine.
scientific article; zbMATH DE number 7022742