Abstract
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 mapsRz,tthat A. F. Beardon proposed, we prove thatRz,thas Fatou components with connectivities 3 and 5 for anyt∈0,1/12. Furthermore, there existst∈0,1/12such thatRz,thas Fatou components with connectivity nine.
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