%0 Journal Article
%T Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps
%A Weiyuan Qiu
%A Fei Yang
%A Yongcheng Yin
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1311.3727v3