cr -动力系统拓扑传递性的一些变化

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-17 DOI:10.1016/j.topol.2025.109482

Nayan Adhikary, Anima Nagar

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引用次数: 0

摘要

我们通过研究一个最古老的动力学性质——传递性来考虑闭合关系的拓扑动力学。我们研究了两种（封闭关系）的正则-动力系统——（X，G），其中关系G≥X×X是封闭的，（X，G，•）给出了合适的封闭关系G的“合适的动力学”，其中X假定为无孤立点的紧度量空间。（X，G）给出了研究一组初始条件初值问题的一般方法，而（X，G，•）给出了研究连续和准连续映射动力学的一般方法。我们观察到闭合关系的动态比地图的动态更丰富，并且发现这些闭合关系的及物性比已知的地图有更多的版本。

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Some variations of topological transitivity for CR-dynamical systems

We consider the topological dynamics of closed relations (CR) by studying one of the oldest dynamical property - ‘transitivity’. We investigate the two kinds of (closed relation) CR-dynamical systems -

(X, G)

where the relation

G \subseteq X \times X

is closed and

(X, G, •)

giving the ‘suitable dynamics’ for a suitable closed relation G, where X is assumed to be a compact metric space without isolated points.

(X, G)

gives a general approach to study initial value problems for a set of initial conditions, whereas

(X, G, •)

gives a general approach to study the dynamics of both continuous and quasi-continuous maps.

We observe that the dynamics of closed relations is richer than the dynamics of maps and find that we have much more versions of transitivity for these closed relations than what is known for maps.

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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.