Rigidity Theorem for Self-Affine Arcs

A. V. Tetenov, O. A. Chelkanova

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)81-84
Number of pages4
JournalDoklady Mathematics
Volume103
Issue number2
DOIs
Publication statusPublished - Mar 2021

Keywords

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

OECD FOS+WOS

  • 1.01 MATHEMATICS

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