Dichotomy theorem for topological semigroup actions

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-12-20 DOI:10.1016/j.topol.2024.109188

Zhumin Ding , Yu Huang , Tao Wang

引用次数: 0

Abstract

We introduce the notions of equi-stable points and equi-asymptotically stable points for topological semigroup actions with a regular system and explore the totally different behaviors of control sets based on these two kinds of points, which are the analogies to the well-known dichotomy theorem for topological transitive dynamical systems. Besides, two illustrative examples are given to show that the equi-asymptotically stable points are different from equi-stable points.

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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.