Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps
Quasisymmetric geometry of the Cantor circles as the Julia sets of rational maps
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DOI：
10.3934/dcds.2016.36.3375
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发表时间：
2013-11
期刊：
影响因子：
--
通讯作者：
Weiyuan Qiu;Fei Yang;Yongcheng Yin
中科院分区：
文献类型：
--
作者：
Weiyuan Qiu;Fei Yang;Yongcheng Yin
本文给出了三类抛物有理映射，并证明了对于适当的参数，作为非双曲有理映射的Julia集的每一个Cantor圆集必须与这三类映射中的一个映射的Julia集拟对称等价.结合前面得到的一个结果，在拟对称等价意义下给出了康托圈Julia集的一个完全分类。研究了Cantor圈Julia集的分支的正则性，给出了Cantor圈Julia集的分支是拟圈的一个充要条件.
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.