纽豪斯厚度、分形交点和图案综述

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Mathematical & Computational Applications Pub Date : 2022-12-05 DOI:10.3390/mca27060111

Alexia Yavicoli

{"title":"纽豪斯厚度、分形交点和图案综述","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":"{\"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}","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

摘要

在这篇文章中，我们引入了一个集合大小的概念，称为厚度，可以用来保证两个Cantor集合相交（Gap引理），并显示厚度、Schmidt对策和模式之间的联系。我们主要是在现实中工作，但我们也在更高维度上介绍这个主题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A Survey on Newhouse Thickness, Fractal Intersections and Patterns

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical & Computational Applications MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

自引率

10.50%

发文量

审稿时长

12 weeks

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.