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

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