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This article is cited in 2 scientific papers (total in 2 papers)
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.
Received May 1, 2018, published July 27, 2018
Citation:
K. G. Kamalutdinov, A. V. Tetenov, “Twofold Cantor sets in $\mathbb{R}$”, Sib. Èlektron. Mat. Izv., 15 (2018), 801–814
Linking options:
https://www.mathnet.ru/eng/semr954 https://www.mathnet.ru/eng/semr/v15/p801
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