The Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps

2012/04/05 by Yang, Fei, Wang, Xiaoguang
#37F10 #37F35 #37F50 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.1282

Abstract

In this paper, we give a formula of the Hausdorff dimension of the boundary of the immediate basin of infinity of McMullen maps f_p(z)=z^Q+p/z^Q, where Q≥ 3 and p is small. This gives a lower bound of the Hausdorff dimension of the Julia sets of McMullen maps in the special cases.

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