论传递算子的谱势，\(\boldsymbol t\) -熵，熵与拓扑压力的关系

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2023-03-17 DOI:10.1134/S1061920823010016

V. I. Bakhtin, A. V. Lebedev

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引用次数: 0

摘要

本文致力于分析动力系统谱理论的主要对象(传递算子和加权移位算子)与信息论和热力学形式主义的基本特征(熵和拓扑压力)之间的关系。我们提出了将这些物体与\(t\) -熵和谱势联系起来的显式公式。在此基础上，我们揭示了逆拉米率的作用，正向熵和一个基本集，以及动力系统的不可收缩性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On Relationships between the Spectral Potential of Transfer Operators, \(\boldsymbol t\)-Entropy, Entropy and Topological Pressure

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.

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

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.