原始替换的子移位的几何表示

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2023-11-03 DOI:10.1017/etds.2023.101

PAUL MERCAT

{"title":"原始替换的子移位的几何表示","authors":"PAUL MERCAT","doi":"10.1017/etds.2023.101","DOIUrl":null,"url":null,"abstract":"Abstract For any primitive substitution whose Perron eigenvalue is a Pisot unit, we construct a domain exchange that is measurably conjugate to the subshift. Additionally, we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitutions, we show that the subshift is either a finite extension of a torus translation or its eigenvalues are roots of unity. Furthermore, we provide an algorithm to compute eigenvalues of the subshift associated with any primitive pseudo-unimodular substitution.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometrical representation of subshifts for primitive substitutions\",\"authors\":\"PAUL MERCAT\",\"doi\":\"10.1017/etds.2023.101\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract For any primitive substitution whose Perron eigenvalue is a Pisot unit, we construct a domain exchange that is measurably conjugate to the subshift. Additionally, we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitutions, we show that the subshift is either a finite extension of a torus translation or its eigenvalues are roots of unity. Furthermore, we provide an algorithm to compute eigenvalues of the subshift associated with any primitive pseudo-unimodular substitution.\",\"PeriodicalId\":50504,\"journal\":{\"name\":\"Ergodic Theory and Dynamical Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-11-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Ergodic Theory and Dynamical Systems\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/etds.2023.101\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ergodic Theory and Dynamical Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/etds.2023.101","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要对于任意一个Perron特征值为Pisot单位的原元替换，我们构造了一个与子位移可测量共轭的域交换。此外，我们还给出了子位移是环面平移的有限扩展的一个条件。对于弱不可约Pisot替换的特殊情况，我们证明了子位移是环面平移的有限扩展，或者它的特征值是单位根。此外，我们还提供了一种计算与任何原始伪单模替换相关的子位移的特征值的算法。

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

Geometrical representation of subshifts for primitive substitutions

Abstract For any primitive substitution whose Perron eigenvalue is a Pisot unit, we construct a domain exchange that is measurably conjugate to the subshift. Additionally, we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitutions, we show that the subshift is either a finite extension of a torus translation or its eigenvalues are roots of unity. Furthermore, we provide an algorithm to compute eigenvalues of the subshift associated with any primitive pseudo-unimodular substitution.

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

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.