Geodesic
Twofold Cantor sets in $\mathbb{R}$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 801-814.

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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
Mots-clés : Hausdorff dimension. 
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K. G. Kamalutdinov; A. V. Tetenov. Twofold Cantor sets in $\mathbb{R}$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 801-814. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a129/

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