Twofold cantor sets in ℝ

Kirill Kamalutdinov; Andrei Tetenov

doi:10.17377/semi.2018.15.066

Twofold cantor sets in ℝ

Kirill Kamalutdinov, Andrei Tetenov

Результат исследования: Научные публикации в периодических изданиях › статья

2 Цитирования (Scopus)

Аннотация

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) ∈ [0, 1/16]² the sets K_pq are twofold Cantor sets.

Язык оригинала	английский
Страницы (с-по)	801-814
Число страниц	14
Журнал	Siberian Electronic Mathematical Reports
Том	15
DOI	https://doi.org/10.17377/semi.2018.15.066
Состояние	Опубликовано - 1 янв 2018

Доступ к документу

10.17377/semi.2018.15.066

Link to publication in Scopus

Fingerprint Подробные сведения о темах исследования «Twofold cantor sets in ℝ». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать

Kamalutdinov, K., & Tetenov, A. (2018). Twofold cantor sets in ℝ. Siberian Electronic Mathematical Reports, 15, 801-814. https://doi.org/10.17377/semi.2018.15.066

@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 = "Siberian Electronic Mathematical Reports",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

}

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 - Siberian Electronic Mathematical Reports

JF - Siberian Electronic Mathematical Reports

SN - 1813-3304

ER -