{"title":"On Relationships between the Spectral Potential of Transfer Operators, \\(\\boldsymbol t\\)-Entropy, Entropy and Topological Pressure","authors":"V. I. Bakhtin, A. V. Lebedev","doi":"10.1134/S1061920823010016","DOIUrl":null,"url":null,"abstract":"<p> The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism (entropy and topological pressure). We present explicit formulas linking these objects with the <span>\\(t\\)</span>-entropy and spectral potential. Herewith we uncover the role of inverse rami-rate, the forward entropy along with an essential set, and the property of noncontractibility of a dynamical system. </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 1","pages":"1 - 24"},"PeriodicalIF":1.7000,"publicationDate":"2023-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823010016","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism (entropy and topological pressure). We present explicit formulas linking these objects with the \(t\)-entropy and spectral potential. Herewith we uncover the role of inverse rami-rate, the forward entropy along with an essential set, and the property of noncontractibility of a dynamical system.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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