Equicontinuity, rigidity, and distality of trajectories

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-16 DOI:10.1016/j.topol.2025.109595

Khadija Ben Rejeb , Seif Mezzi

引用次数: 0

Abstract

A dynamical system

(X, f)

induces in a natural way two interesting dynamical systems worth studying. One is the system

(T, f_{T})

induced on the closure T of all trajectories of f equipped with the Hausdorff metric, and the other one is induced on the space S of all orbits of f equipped with the product topology. In this paper, we study equicontinuity, rigidity and distality for both induced systems, and we investigate the connection of these properties among these induced systems and the original system

(X, f)

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轨迹的等连续性、刚性和距离性

一个动力系统（X,f）以一种自然的方式归纳出两个有趣的值得研究的动力系统。一个是在具有Hausdorff度规的f的所有轨迹的闭包T上导出的系统（T,fT），另一个是在具有积拓扑的f的所有轨道的空间S上导出的系统。本文研究了两种诱导系统的等连续性、刚性和远性，并研究了这些诱导系统与原系统（X,f）之间这些性质的联系。

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.