Quasisymmetries of Sierpiński carpet Julia sets

Mario Bonk; Mikhail Lyubich; Sergei Merenkov

doi:10.1016/j.aim.2016.06.007

Quasisymmetries of Sierpiński carpet Julia sets

Mario Bonk
, Mikhail Lyubich
, Sergei Merenkov

Mathematical Science Institute

Stony Brook University

University of California at Los Angeles
City University of New York

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We prove that if ξ is a quasisymmetric homeomorphism between Sierpiński carpets that are Julia sets of postcritically-finite rational maps, then ξ is the restriction of a Möbius transformation. This implies that the group of quasisymmetric homeomorphisms of a Sierpiński carpet Julia set of a postcritically-finite rational map is finite.

Original language	English
Pages (from-to)	383-422
Number of pages	40
Journal	Advances in Mathematics
Volume	301
DOIs	https://doi.org/10.1016/j.aim.2016.06.007
State	Published - Oct 1 2016

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title = "Quasisymmetries of Sierpi{\'n}ski carpet Julia sets",

abstract = "We prove that if ξ is a quasisymmetric homeomorphism between Sierpi{\'n}ski carpets that are Julia sets of postcritically-finite rational maps, then ξ is the restriction of a M{\"o}bius transformation. This implies that the group of quasisymmetric homeomorphisms of a Sierpi{\'n}ski carpet Julia set of a postcritically-finite rational map is finite.",

author = "Mario Bonk and Mikhail Lyubich and Sergei Merenkov",

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AU - Bonk, Mario

AU - Lyubich, Mikhail

AU - Merenkov, Sergei

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Y1 - 2016/10/1

N2 - We prove that if ξ is a quasisymmetric homeomorphism between Sierpiński carpets that are Julia sets of postcritically-finite rational maps, then ξ is the restriction of a Möbius transformation. This implies that the group of quasisymmetric homeomorphisms of a Sierpiński carpet Julia set of a postcritically-finite rational map is finite.

AB - We prove that if ξ is a quasisymmetric homeomorphism between Sierpiński carpets that are Julia sets of postcritically-finite rational maps, then ξ is the restriction of a Möbius transformation. This implies that the group of quasisymmetric homeomorphisms of a Sierpiński carpet Julia set of a postcritically-finite rational map is finite.

UR - https://www.scopus.com/pages/publications/84976569022

U2 - 10.1016/j.aim.2016.06.007

DO - 10.1016/j.aim.2016.06.007

M3 - Article

SN - 0001-8708

VL - 301

SP - 383

EP - 422

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Quasisymmetries of Sierpiński carpet Julia sets

Abstract

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