Local fibrations of topological entropy for fibred systems

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-10-23 DOI:10.1016/j.topol.2024.109114

Zhongxuan Yang, Jiajun Zhang

引用次数: 0

Abstract

Given a fibred dynamical system, we introduce the notions of entropy fiber of a fibre for topological entropy, Bowen entropy and packing entropy, which quantifies the “infinitesimal change” in the dynamics of a fibre with respect to its neighboring fibres, this gives rise to an (upper semicontinuous) fibre function. Besides, we show that the topological entropy (Bowen entropy and packing entropy, resp.) of the system is the supremum of the topological entropy fiber (Bowen entropy and packing entropy, resp.) of its fibres, which provides a new perspective on the study of entropy in fibred systems.

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纤维系统拓扑熵的局部纤维化

给定一个纤维动态系统，我们引入了拓扑熵、鲍文熵和堆积熵的纤维熵纤维的概念，它量化了一个纤维相对于其相邻纤维的动态 "无穷小变化"，这就产生了一个（上半连续）纤维函数。此外，我们还证明了系统的拓扑熵（鲍文熵和堆积熵）是其纤维的拓扑熵纤维（鲍文熵和堆积熵）的上位，这为研究纤维系统中的熵提供了一个新视角。

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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