2017/08/19 by Yang, Fei
#37F30 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F45 #Secondary 37F10
paper · doi:10.48550/arxiv.1708.05848
It was known that the Sierpiński carpets can appear as the Julia sets in the families of some rational maps. In this article we present a criterion that guarantees the existence of the carpet Julia sets in some rational maps having exactly one fixed (super-) attracting or parabolic basin. We show that this criterion can be applied to some well known rational maps, such as McMullen maps and Morosawa-Pilgrim family. Moreover, we give also some special examples whose Julia sets are Sierpiński carpets.