Quasisymmetries of Sierpinski carpet Julia sets

被引：19

作者：

Bonk, Mario ^{[1
]}

Lyubich, Mikhail ^{[2
]}

Merenkov, Sergei ^{[3
]}

机构：

[1] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[2] SUNY Stony Brook, Inst Math Sci, Stony Brook, NY 11794 USA

[3] CUNY City Coll, Dept Math, New York, NY 10031 USA

来源：

ADVANCES IN MATHEMATICS | 2016年 / 301卷

关键词：

RATIONAL FUNCTIONS; LOCAL RIGIDITY; SCHOTTKY SETS; MAPS;

D O I：

10.1016/j.aim.2016.06.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that if xi a quasisymmetric homeomorphism between Sierpinski carpets that are Julia sets of postcriticallyfinite rational maps, then xi is the restriction of a Mobius transformation. This implies that the group of quasisymmetric homeomorphisms of a Sierpinski carpet Julia set of a postcritically-finite rational map is finite. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：383 / 422

页数：40

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