{"title":"Variational principle of metric mean dimension and rate distortion dimension for amenable group actions","authors":"Junye Li, Yong Ji, Tian Zhan, Yuanyuan Zhang","doi":"10.1016/j.jmaa.2025.129282","DOIUrl":null,"url":null,"abstract":"<div><div>Recently, Wang has demonstrated some new variational relationships for metric mean dimension and rate distortion dimension. In this paper, we mainly consider the actions of amenable group. The variational principle between local entropy and Bowen metric mean dimension was given. We also give new characteristics of rate distortion dimension. Finally, we consider Bowen metric mean dimension of the generic point set.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"546 1","pages":"Article 129282"},"PeriodicalIF":1.2000,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25000630","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Recently, Wang has demonstrated some new variational relationships for metric mean dimension and rate distortion dimension. In this paper, we mainly consider the actions of amenable group. The variational principle between local entropy and Bowen metric mean dimension was given. We also give new characteristics of rate distortion dimension. Finally, we consider Bowen metric mean dimension of the generic point set.
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The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
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