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 that A. F. Beardon proposed, we prove that has Fatou components with connectivities 3 and 5 for any . Furthermore, there exists such that has Fatou components with connectivity nine.
"On Connectivity of Fatou Components concerning a Family of Rational Maps." Abstr. Appl. Anal. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/621312