Quasisymmetries of Sierpiński carpet Julia sets

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 postcri...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2016-10, Vol.301, p.383-422
Main Authors: Bonk, Mario, Lyubich, Mikhail, Merenkov, Sergei
Format: Article
Language:English
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Summary: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.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2016.06.007