A. V. Tetenov, O. A. Chelkanova, “Rigidity theorem for self-affine arcs”, Dokl. RAN. Math. Inf. Proc. Upr., 2021, Volume 497,Pages <nobr>18

This article is cited in 1 paper

MATHEMATICS

Rigidity theorem for self-affine arcs

A. V. Tetenov^abc, O. A. Chelkanova^b

^a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
^b Gorno-Altaisk State University, Gorno-Altaisk, Russia
^c Novosibirsk State University, Novosibirsk, Russia

Abstract: It has been known for more than a decade that, if a self-similar arc $\gamma$ can be shifted along itself by similarity maps that are arbitrarily close to identity, then $\gamma$ 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: self-affine arc, attractor, weak separation property, rigidity theorem.

UDC: 517.54

Presented: Yu. G. Reshetnyak
Received: 24.12.2020
Revised: 11.01.2021
Accepted: 26.01.2021

DOI: 10.31857/S2686954321020053