Quasisymmetric geometry of Sierpiński carpet Julia sets
Quasisymmetric geometry of Sierpiński carpet Julia sets
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DOI：
10.4064/fm494-12-2017
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发表时间：
2014-03
影响因子：
0.6
通讯作者：
Weiyuan Qiu;Fei Yang;Jinsong Zeng
中科院分区：
文献类型：
--
作者：
Weiyuan Qiu;Fei Yang;Jinsong Zeng
本文主要关注具有非循环临界点的有理图的谢尔宾斯基地毯朱莉娅集。我们研究了外围圆的均匀拟圆特性、外围圆的相对分离特性以及这些地毯的局部多孔特性。我们还建立了这些地毯的一些拟对称刚度，将 Bonk-Lyubich-Merenkov 的主要结果推广到后临界无限情况。最后，我们给出了构造一类后临界无限有理图的策略，其朱莉娅集拟对称地等价于一些圆形地毯。
In this paper, the main focus is on the Sierpinski carpet Julia sets of the rational maps with non-recurrent critical points. We study the uniform quasicircle property of the peripheral circles, the relatively separated property of the peripheral circles and the locally porous property of these carpets. We also establish some quasisymmetric rigidities of these carpets, which generalizes the main results of Bonk-Lyubich-Merenkov to the postcritically infinite case. In the end we give a strategy to construct a class of postcritically infinite rational maps whose Julia sets are quasisymetrically equivalent to some round carpets.