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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 801–814 (Mi semr954)  

Real, complex and functional analysis

Twofold Cantor sets in $\mathbb{R}$

K. G. Kamalutdinova, A. V. Tetenovab

a Novosibirsk State University, Novosibirsk, Russia
b Gorno-Altaisk State University

Abstract: A symmetric Cantor set $K_{pq}$ in $[0,1]$ with double fixed points 0 and 1 and contraction ratios p and q is called twofold Cantor set if it satisfies special exact overlap condition. We prove that all twofold Cantor sets have isomorphic self-similar structures and do not have weak separation property and that for Lebesgue-almost all $(p,q)\in [0,1/16]^2$ the sets $K_{pq}$ are twofold Cantor sets.

Keywords: self-similar set, weak separation property, twofold Cantor set, Hausdorff dimension.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00414_а
18-501-51021_НИФ_а
The research of authors was supported by Russian Foundation of Basic Research grants No. 16-01-00414, No. 18-501-51021.


DOI: https://doi.org/10.17377/semi.2018.15.066

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Bibliographic databases:

Document Type: Article
UDC: 515.17
MSC: 28A80
Received May 1, 2018, published July 27, 2018
Language: English

Citation: K. G. Kamalutdinov, A. V. Tetenov, “Twofold Cantor sets in $\mathbb{R}$”, Sib. Èlektron. Mat. Izv., 15 (2018), 801–814

Citation in format AMSBIB
\Bibitem{KamTet18}
\by K.~G.~Kamalutdinov, A.~V.~Tetenov
\paper Twofold Cantor sets in $\mathbb{R}$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 801--814
\mathnet{http://mi.mathnet.ru/semr954}
\crossref{https://doi.org/10.17377/semi.2018.15.066}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454860200008}


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