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Twofold cantor sets in ℝ. / Kamalutdinov, Kirill; Tetenov, Andrei.

In: Сибирские электронные математические известия, Vol. 15, 01.01.2018, p. 801-814.

Research output: Contribution to journal › Article › peer-review

Harvard

Kamalutdinov, K & Tetenov, A 2018, 'Twofold cantor sets in ℝ', Сибирские электронные математические известия, vol. 15, pp. 801-814. https://doi.org/10.17377/semi.2018.15.066

APA

Kamalutdinov, K., & Tetenov, A. (2018). Twofold cantor sets in ℝ. Сибирские электронные математические известия, 15, 801-814. https://doi.org/10.17377/semi.2018.15.066

Vancouver

Kamalutdinov K, Tetenov A. Twofold cantor sets in ℝ. Сибирские электронные математические известия. 2018 Jan 1;15:801-814. doi: 10.17377/semi.2018.15.066

Author

Kamalutdinov, Kirill ; Tetenov, Andrei. / Twofold cantor sets in ℝ. In: Сибирские электронные математические известия. 2018 ; Vol. 15. pp. 801-814.

BibTeX

@article{f99fbf0c924a43adb2b9ec224379807c,
title = "Twofold cantor sets in ℝ",
abstract = "A symmetric Cantor set Kpq 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) ∈ [0, 1/16]2 the sets Kpq are twofold Cantor sets.",
keywords = "Hausdorff dimension, Self-similar set, Twofold Cantor set, Weak separation property, HAUSDORFF DIMENSION, FRACTALS, self-similar set, SELF-SIMILAR SETS, SYSTEMS, weak separation property, twofold Cantor set",
author = "Kirill Kamalutdinov and Andrei Tetenov",
year = "2018",
month = jan,
day = "1",
doi = "10.17377/semi.2018.15.066",
language = "English",
volume = "15",
pages = "801--814",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Twofold cantor sets in ℝ

AU - Kamalutdinov, Kirill

AU - Tetenov, Andrei

PY - 2018/1/1

Y1 - 2018/1/1

N2 - A symmetric Cantor set Kpq 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) ∈ [0, 1/16]2 the sets Kpq are twofold Cantor sets.

AB - A symmetric Cantor set Kpq 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) ∈ [0, 1/16]2 the sets Kpq are twofold Cantor sets.

KW - Hausdorff dimension

KW - Self-similar set

KW - Twofold Cantor set

KW - Weak separation property

KW - HAUSDORFF DIMENSION

KW - FRACTALS

KW - self-similar set

KW - SELF-SIMILAR SETS

KW - SYSTEMS

KW - weak separation property

KW - twofold Cantor set

UR - http://www.scopus.com/inward/record.url?scp=85074899858&partnerID=8YFLogxK

U2 - 10.17377/semi.2018.15.066

DO - 10.17377/semi.2018.15.066

M3 - Article

AN - SCOPUS:85074899858

VL - 15

SP - 801

EP - 814

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 22473553