Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps
Weiyuan Qiu Fei Yang Yongcheng Yin
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.
keywords: quasisymmetrically equivalent. Cantor circles Julia sets

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