Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Dokl. RAN. Math. Inf. Proc. Upr.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 497, Pages 18–22
DOI: https://doi.org/10.31857/S2686954321020053 (Mi danma164) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Rigidity theorem for self-affine arcs

A. V. Tetenovabc, O. A. Chelkanovab

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
Full-text PDF (135 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.31857/S2686954321020053
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.
Funding agency Grant number
Mathematical Center in Akademgorodok 075-15-2019-1613
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.
Presented: Yu. G. Reshetnyak
Received: 24.12.2020
Revised: 11.01.2021
Accepted: 26.01.2021
English version:
Doklady Mathematics, 2021, Volume 103, Issue 2, Pages 81–84
DOI: https://doi.org/10.1134/S1064562421020058
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
Citation: A. V. Tetenov, O. A. Chelkanova, “Rigidity theorem for self-affine arcs”, Dokl. RAN. Math. Inf. Proc. Upr., 497 (2021), 18–22; Dokl. Math., 103:2 (2021), 81–84
Citation in format AMSBIB
\Bibitem{TetChe21}
\by A.~V.~Tetenov, O.~A.~Chelkanova
\paper Rigidity theorem for self-affine arcs
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2021
\vol 497
\pages 18--22
\mathnet{http://mi.mathnet.ru/danma164}
\crossref{https://doi.org/10.31857/S2686954321020053}
\zmath{https://zbmath.org/?q=an:7424705}
\elib{https://elibrary.ru/item.asp?id=45683730}
\transl
\jour Dokl. Math.
\yr 2021
\vol 103
\issue 2
\pages 81--84
\crossref{https://doi.org/10.1134/S1064562421020058}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85111125614}
Linking options:
  • https://www.mathnet.ru/eng/danma164
  • https://www.mathnet.ru/eng/danma/v497/p18
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
    Statistics & downloads:
    Abstract page:106
    Full-text PDF :23
    References:21
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024