关于具有阴影特性的完全不规则地图集

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-07-25 DOI:10.1016/j.topol.2024.109025

M. Carvalho , V. Coelho , L. Salgado

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引用次数: 0

摘要

我们证明，对于每一个满足阴影属性并作用于没有孤立点的紧凑度量空间的非唯一遍历传递连续映射来说，完全不规则集都是拜尔泛函。我们还证明，在前面的假设条件下，每个完全不规则点的轨道都是密集的。之后，我们分析了反演性与阴影性质之间的联系，得出了它们在广延同构系中共同作用的一些结果，并讨论了几个例子来检验我们结果的范围。

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On the completely irregular set of maps with the shadowing property

We prove that the completely irregular set is Baire generic for every non-uniquely ergodic transitive continuous map which satisfies the shadowing property and acts on a compact metric space without isolated points. We also show that, under the previous assumptions, the orbit of every completely irregular point is dense. Afterwards, we analyze the connection between transitivity and the shadowing property, draw a few consequences of their joint action within the family of expansive homeomorphisms, and discuss several examples to test the scope of our results.

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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.