Rigidity Theorem for Self-Affine Arcs

Rigidity Theorem for Self-Affine Arcs Full article

Journal

Doklady Mathematics
ISSN: 1064-5624 , E-ISSN: 1531-8362

Output data

Year: 2021, Volume: 103, Number: 2, Pages: 81-84 Pages count : 4 DOI: 10.1134/S1064562421020058

Tags

attractor; rigidity theorem; self-affine arc; weak separation property

Authors

Tetenov A.V. ^1,2,3 , Chelkanova O.A. ²

Affiliations

1	Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Novosibirsk, 630090, Russian Federation
3	Gorno-Altaisk State University, Gorno-Altaisk, 649000, Russian Federation

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.

Tetenov A.V. , Chelkanova O.A.
Rigidity Theorem for Self-Affine Arcs
Doklady Mathematics. 2021. V.103. N2. P.81-84. DOI: 10.1134/S1064562421020058 WOS Scopus OpenAlex

Web of science:	WOS:000673209700004
Scopus:	2-s2.0-85111125614
OpenAlex:	W3197486249

DB	Citing
Scopus	1
OpenAlex	1
Web of science	1