A new entropy on metric spaces with respect to Bourbaki-bounded subsets

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-10-31 DOI:10.1016/j.topol.2024.109128

H.M.H. Zarenezhad, Javad Jamalzadeh

引用次数: 0

Abstract

In this paper, we define a new entropy for every self-map on metric spaces, which is referred to as the Bourbaki entropy. We show, by means of an example, that the metric entropy is not necessarily equal to the Bourbaki entropy. Finally, the basic properties of the Bourbaki entropy are studied. The obtained results include the logarithmic law, invariance under conjugation, the weak addition theorem, and the completion theorem.

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关于bourbaki有界子集的度量空间上的新熵

本文对度量空间上的每一个自映射定义了一个新的熵，称为布尔巴基熵。我们通过一个例子证明，度规熵不一定等于布尔巴基熵。最后，研究了布尔巴基熵的基本性质。得到的结果包括对数定律、共轭不变性、弱加法定理和补全定理。

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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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.

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