{"title":"On the structure of self-affine Jordan arcs in ℝ2","authors":"A. Tetenov, Allanazar Kutlimuratov","doi":"10.1515/dema-2022-0228","DOIUrl":null,"url":null,"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 γ \\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.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/dema-2022-0228","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
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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 γ \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.
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