Specification in Mahavier systems via closed relations

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2026-03-15 Epub Date: 2026-01-27 DOI:10.1016/j.topol.2026.109742

Iztok Banič , Goran Erceg , Ivan Jelić , Judy Kennedy

引用次数: 0

Abstract

We study two fundamental properties of topological dynamical systems, the specification property and the initial specification property, and explore their generalizations to the broader setting of CR-dynamical systems, where the dynamics are governed by closed relations rather than continuous functions. While these two properties are equivalent for many classical systems, we demonstrate that their generalizations to CR-dynamical systems often lead to distinct behaviors. Applying them to Mahavier dynamical systems, we introduce new specification-type properties. These generalized notions extend the classical theory and reveal rich structural differences in dynamical behavior. Moreover, each of the new properties reduces to the standard specification property when restricted to continuous functions.

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通过闭合关系的Mahavier系统规范

我们研究了拓扑动力系统的两个基本性质，即规范性质和初始规范性质，并探讨了它们在更广泛的cr -动力系统中的推广，在cr -动力系统中，动力学由封闭关系而不是连续函数控制。虽然这两个性质对于许多经典系统是等价的，但我们证明了它们在cr -动力系统中的推广通常会导致不同的行为。将它们应用于Mahavier动力系统，我们引入了新的规范型性质。这些广义概念扩展了经典理论，揭示了动力学行为的丰富结构差异。此外，当限制于连续函数时，每个新性质都简化为标准规范性质。

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.