On the structure of self-affine Jordan arcs in ℝ<sup>2</sup>-Reference-Cited by-同舟云学术

On the structure of self-affine Jordan arcs in ℝ²

Published:2023-01-01 Issue:1 Volume:56 Page:
ISSN:2391-4661
Container-title:Demonstratio Mathematica
language:en
Short-container-title:

Author:

Tetenov Andrei¹,Kutlimuratov Allanazar²

Affiliation:

1. Sobolev Mathematical Institute , 630090 Novosibirsk , Russia

2. Chirchik State Pedagogical University , 111700 Chirchik , Uzbekistan

Abstract

Abstract We prove that if a self-affine arc

γ ∈ R 2

\gamma \in {{\mathbb{R}}}^{2}

does not satisfy weak separation condition, then it is a segment of a parabola or a straight line. If a self-affine arc

\gamma

is not a segment of a parabola or a line, then it is a component of the attractor of a Jordan multizipper with the same set of generators.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/dema-2022-0228/pdf

Reference33 articles.

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2. V. V. Aseev, A. V. Tetenov, and A. S. Kravchenko, On self-similar Jordan curves on the plane, Siberian Math. J. 44 (2003), no. 4, 481–492, DOI: https://doi.org/10.1023/A:1023848327898.

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5. P. Levy, Les courbes planes ou gauches et les surfaces composees de parties semblables au tout, J. Ecole Polytechn., III. Ser. 144 (1938), 227–247 et 249–291.

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