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 › рецензирование

3 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	Сибирские электронные математические известия
Том	15
DOI	https://doi.org/10.17377/semi.2018.15.066
Состояние	Опубликовано - 1 янв. 2018

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10.17377/semi.2018.15.066

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

В: Сибирские электронные математические известия, Том 15, 01.01.2018, стр. 801-814.

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

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AU - Tetenov, Andrei

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Y1 - 2018/1/1

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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.

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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

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Twofold cantor sets in ℝ

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