论有限类型树状移动的稳定性和阴影

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-03-09 DOI:10.1090/proc/16831

Dawid Bucki

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引用次数: 0

摘要

我们研究了树移法的伪轨道追踪性质、拓扑稳定性和开放性之间的关系。我们证明，当且仅当一个树移位具有伪轨道追踪性质时，它才是有限类型的，这意味着该树移位在拓扑上是稳定的，并且所有移位映射都是开放的。我们还举例说明了一个所有移位映射都是开放的但不是有限类型的树移位。我们还发现，如果拓扑上稳定的树移位没有孤立点，那么它就是有限类型的。

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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On the stability and shadowing of tree-shifts of finite type

We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that the tree-shift is topologically stable and all shift maps are open. We also present an example of a tree-shift for which all shift maps are open but which is not of finite type. It also turns out that if a topologically stable tree-shift does not have isolated points then it is of finite type.

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.