Rigidity Theorem for Self-Affine Arcs

A. V. Tetenov; O. A. Chelkanova

doi:10.1134/S1064562421020058

Rigidity Theorem for Self-Affine Arcs

A. V. Tetenov, O. A. Chelkanova

Кафедра теории функций ММФ

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

Аннотация

It has been known for more than a decade that, if a self-similar arc γ can be shifted along itself by similarity maps that are arbitrarily close to identity, then γ is a straight line segment. We extend this statement to the class of self-affine arcs and prove that each self-affine arc admitting affine shifts that may be arbitrarily close to identity is a segment of a parabola or a straight line.

Язык оригинала	английский
Страницы (с-по)	81-84
Число страниц	4
Журнал	Doklady Mathematics
Том	103
Номер выпуска	2
DOI	https://doi.org/10.1134/S1064562421020058
Состояние	Опубликовано - мар 2021

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abstract = "It has been known for more than a decade that, if a self-similar arc γ can be shifted along itself by similarity maps that are arbitrarily close to identity, then γ is a straight line segment. We extend this statement to the class of self-affine arcs and prove that each self-affine arc admitting affine shifts that may be arbitrarily close to identity is a segment of a parabola or a straight line.",

keywords = "attractor, rigidity theorem, self-affine arc, weak separation property",

author = "Tetenov, {A. V.} and Chelkanova, {O. A.}",

note = "Funding Information: This work was supported by the Mathematical Center in Akademgorodok with the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-15-2019-1613. Publisher Copyright: {\textcopyright} 2021, Pleiades Publishing, Ltd.",

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AU - Chelkanova, O. A.

N1 - Funding Information: This work was supported by the Mathematical Center in Akademgorodok with the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-15-2019-1613. Publisher Copyright: © 2021, Pleiades Publishing, Ltd.

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N2 - It has been known for more than a decade that, if a self-similar arc γ can be shifted along itself by similarity maps that are arbitrarily close to identity, then γ is a straight line segment. We extend this statement to the class of self-affine arcs and prove that each self-affine arc admitting affine shifts that may be arbitrarily close to identity is a segment of a parabola or a straight line.

AB - It has been known for more than a decade that, if a self-similar arc γ can be shifted along itself by similarity maps that are arbitrarily close to identity, then γ is a straight line segment. We extend this statement to the class of self-affine arcs and prove that each self-affine arc admitting affine shifts that may be arbitrarily close to identity is a segment of a parabola or a straight line.

KW - attractor

KW - rigidity theorem

KW - self-affine arc

KW - weak separation property

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M3 - Article

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JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -

Rigidity Theorem for Self-Affine Arcs

Аннотация

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