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Rigidity Theorem for Self-Affine Arcs. / Tetenov, A. V.; Chelkanova, O. A.

In: Doklady Mathematics, Vol. 103, No. 2, 03.2021, p. 81-84.

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

Harvard

Tetenov, AV & Chelkanova, OA 2021, 'Rigidity Theorem for Self-Affine Arcs', Doklady Mathematics, vol. 103, no. 2, pp. 81-84. https://doi.org/10.1134/S1064562421020058

APA

Tetenov, A. V., & Chelkanova, O. A. (2021). Rigidity Theorem for Self-Affine Arcs. Doklady Mathematics, 103(2), 81-84. https://doi.org/10.1134/S1064562421020058

Vancouver

Tetenov AV, Chelkanova OA. Rigidity Theorem for Self-Affine Arcs. Doklady Mathematics. 2021 Mar;103(2):81-84. doi: 10.1134/S1064562421020058

Author

Tetenov, A. V. ; Chelkanova, O. A. / Rigidity Theorem for Self-Affine Arcs. In: Doklady Mathematics. 2021 ; Vol. 103, No. 2. pp. 81-84.

BibTeX

@article{5b43807a3f654f5eb2eefc2dd9690986,
title = "Rigidity Theorem for Self-Affine Arcs",
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.",
year = "2021",
month = mar,
doi = "10.1134/S1064562421020058",
language = "English",
volume = "103",
pages = "81--84",
journal = "Doklady Mathematics",
issn = "1064-5624",
publisher = "Maik Nauka-Interperiodica Publishing",
number = "2",

}

RIS

TY - JOUR

T1 - Rigidity Theorem for Self-Affine Arcs

AU - Tetenov, A. V.

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.

PY - 2021/3

Y1 - 2021/3

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

UR - http://www.scopus.com/inward/record.url?scp=85111125614&partnerID=8YFLogxK

U2 - 10.1134/S1064562421020058

DO - 10.1134/S1064562421020058

M3 - Article

AN - SCOPUS:85111125614

VL - 103

SP - 81

EP - 84

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 2

ER -

ID: 34174698