{"title":"Variational principle for metric mean dimension with potential","authors":"Yunping Wang, Qianhui He","doi":"10.1080/10236198.2023.2242518","DOIUrl":null,"url":null,"abstract":"In this paper, we study metric mean dimension with potential and set up a variational principle for it, which connects rate distortion function to metric mean dimension with potential. Moreover, we give alternative definitions of metric mean dimensions with potential and show that classic metric mean dimension with potential is equal to Bowen upper and lower capacity metric mean dimensions with potential.","PeriodicalId":15616,"journal":{"name":"Journal of Difference Equations and Applications","volume":"308 ","pages":"657 - 681"},"PeriodicalIF":1.1000,"publicationDate":"2023-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Difference Equations and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/10236198.2023.2242518","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we study metric mean dimension with potential and set up a variational principle for it, which connects rate distortion function to metric mean dimension with potential. Moreover, we give alternative definitions of metric mean dimensions with potential and show that classic metric mean dimension with potential is equal to Bowen upper and lower capacity metric mean dimensions with potential.
期刊介绍：
Journal of Difference Equations and Applications presents state-of-the-art papers on difference equations and discrete dynamical systems and the academic, pure and applied problems in which they arise. The Journal is composed of original research, expository and review articles, and papers that present novel concepts in application and techniques.
The scope of the Journal includes all areas in mathematics that contain significant theory or applications in difference equations or discrete dynamical systems.
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