Various notions of shadowing in triangular system and its component systems

IF 0.6 4区数学 Q3 MATHEMATICS Topology and its Applications Pub Date : 2024-10-18 DOI:10.1016/j.topol.2024.109109

Deepanshu Dhawan, Puneet Sharma

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Abstract

In this article, we investigate various forms of shadowing for a general triangular system. In particular, we relate various notions of shadowing for a triangular system with various notions of shadowing in the component systems. We prove that if the base f for T is transitive then shadowing in the base map and the non-autonomous system generated by a transitive point ensures shadowing of the triangular system. We prove that if the base map for T is expansive then shadowing in the triangular system ensures shadowing in the component systems. We prove that if the non-autonomous component systems form a synchronized family and the base map possesses a globally attracting fixed point

x_{0}

then eventual shadowing in system generated by

x_{0}

ensures eventual shadowing in each of the non-autonomous component systems. We also investigate chain transitivity and chain mixing for a general triangular system.

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三角形系统及其组成系统中的各种阴影概念

在本文中，我们研究了一般三角形系统的各种阴影形式。特别是，我们将三角形系统中的各种阴影概念与组成系统中的各种阴影概念联系起来。我们证明，如果 T 的基图 f 是反式的，那么基图和反式点生成的非自治系统中的阴影就能确保三角形系统的阴影。我们证明，如果 T 的基映射是广延性的，那么三角形系统中的阴影就能确保组件系统中的阴影。我们证明，如果非自治成分系统形成一个同步族，且基图具有一个全局吸引定点 x0，那么由 x0 生成的系统中的最终阴影会确保每个非自治成分系统中的最终阴影。我们还研究了一般三角形系统的链传递性和链混合性。

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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