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LIPSCHITZ EQUIVALENCE OF CANTOR SETS AND IRREDUCIBILITY OF POLYNOMIALS

Part of: Classical measure theory Algebraic number theory: global fields

Published online by Cambridge University Press:  26 June 2018

Jun Jason Luo ,
Huo-Jun Ruan  and
Yi-Lin Wang
Jun Jason Luo
Affiliation:
College of Mathematics and Statistics, Chongqing University, 401331 Chongqing, China Institut für Mathematik, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany email [email protected]
Huo-Jun Ruan
Affiliation:
School of Mathematical Science, Zhejiang University, Hangzhou 310027, China email [email protected]
Yi-Lin Wang
Affiliation:
College of Mathematics and Statistics, Chongqing Uinversity, Chongqing 401331, China email [email protected]
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Abstract

In the paper, we provide an effective criterion for the Lipschitz equivalence of two-branch Cantor sets and three-branch Cantor sets by studying the irreducibility of polynomials. We also find that any two Cantor sets are Lipschitz equivalent if and only if their contraction vectors are equivalent provided one of the contraction vectors is homogeneous.

MSC classification

Primary: 28A80: Fractals
Secondary: 11R09: Polynomials (irreducibility, etc.)
Type
Research Article
Information
Mathematika , Volume 64 , Issue 3 , 2018 , pp. 730 - 741
Copyright
Copyright © University College London 2018 

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Footnotes

The research of Luo and Wang is supported in part by NSFC (no. 11301322), the Fundamental and Frontier Research Project of Chongqing (no. cstc2015jcyjA00035), the Fundamental Research Funds for the Central Universities (no. 106112017CDJXY100005). The research of Ruan is supported in part by NSFC (nos. 11271327, 11771391) and ZJNSFC (no. LR14A010001).

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