重复Delone集壳上有界距离等价类的数目

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-01-07 DOI:10.3934/dcds.2021157

D. Frettloh, A. Garber, L. Sadun

{"title":"重复Delone集壳上有界距离等价类的数目","authors":"D. Frettloh, A. Garber, L. Sadun","doi":"10.3934/dcds.2021157","DOIUrl":null,"url":null,"abstract":"Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"266 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Number of bounded distance equivalence classes in hulls of repetitive Delone sets\",\"authors\":\"D. Frettloh, A. Garber, L. Sadun\",\"doi\":\"10.3934/dcds.2021157\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many.\",\"PeriodicalId\":11254,\"journal\":{\"name\":\"Discrete & Continuous Dynamical Systems - S\",\"volume\":\"266 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete & Continuous Dynamical Systems - S\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/dcds.2021157\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete & Continuous Dynamical Systems - S","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/dcds.2021157","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 5

摘要

如果两个Delone集合之间存在双射，使得对应点的距离一致有界，则两个Delone集合是有界距离等价的。有界距离等价是一种等价关系。我们证明了具有有限局部复杂度的重复Delone集合的壳要么有一个等价类，要么有无数个等价类。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Number of bounded distance equivalence classes in hulls of repetitive Delone sets

Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many.

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

Discrete & Continuous Dynamical Systems - S

自引率

0.00%

发文量