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 -