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. 
@article{SEMR_2018_15_a129,
     author = {K. G. Kamalutdinov and A. V. Tetenov},
     title = {Twofold {Cantor} sets in $\mathbb{R}$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {801--814},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a129/}
}
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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/