{"title":"A Survey on Newhouse Thickness, Fractal Intersections and Patterns","authors":"Alexia Yavicoli","doi":"10.3390/mca27060111","DOIUrl":null,"url":null,"abstract":"In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real line, but we also introduce the topic in higher dimensions.","PeriodicalId":53224,"journal":{"name":"Mathematical & Computational Applications","volume":" ","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical & Computational Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/mca27060111","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 2
Abstract
In this article, we introduce a notion of size for sets, called the thickness, that can be used to guarantee that two Cantor sets intersect (the Gap Lemma) and show a connection among thickness, Schmidt games and patterns. We work mostly in the real line, but we also introduce the topic in higher dimensions.
期刊介绍：
Mathematical and Computational Applications (MCA) is devoted to original research in the field of engineering, natural sciences or social sciences where mathematical and/or computational techniques are necessary for solving specific problems. The aim of the journal is to provide a medium by which a wide range of experience can be exchanged among researchers from diverse fields such as engineering (electrical, mechanical, civil, industrial, aeronautical, nuclear etc.), natural sciences (physics, mathematics, chemistry, biology etc.) or social sciences (administrative sciences, economics, political sciences etc.). The papers may be theoretical where mathematics is used in a nontrivial way or computational or combination of both. Each paper submitted will be reviewed and only papers of highest quality that contain original ideas and research will be published. Papers containing only experimental techniques and abstract mathematics without any sign of application are discouraged.
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