2013/11/15 by Qiu, Weiyuan, Yang, Fei, Yin, Yongcheng
#37F10 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37F45 #Secondary 37F20
paper · doi:10.48550/arxiv.1311.3727
We give three families of parabolic rational maps and show that every Cantor set of circles as the Julia set of a non-hyperbolic rational map must be quasisymmetrically equivalent to the Julia set of one map in these families for suitable parameters. Combining a result obtained before, we give a complete classification of the Cantor circles Julia sets in the sense of quasisymmetric equivalence. Moreover, we study the regularity of the components of the Cantor circles Julia sets and establish a sufficient and necessary condition when a component of a Cantor circles Julia set is a quasicircle.