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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the stability and shadowing of tree-shifts of finite type
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by Dawid Bucki;
Proc. Amer. Math. Soc. 152 (2024), 3509-3520
DOI: https://doi.org/10.1090/proc/16831
Published electronically: June 18, 2024

Previous version: Original version posted June 18, 2024
Corrected version: This version corrects an error in author metadata.

Abstract:

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.
References
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Bibliographic Information
  • Dawid Bucki
  • Affiliation: Faculty of Mathematics and Computer Science & Doctoral School of Exact and Natural Sciences, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland
  • ORCID: 0009-0003-2583-3009
  • Email: dawid.bucki@doctoral.uj.edu.pl
  • Received by editor(s): June 13, 2023
  • Received by editor(s) in revised form: June 21, 2023, December 19, 2023, February 8, 2024, and February 13, 2024
  • Published electronically: June 18, 2024
  • Additional Notes: In the final stages of this research, the author was supported by National Science Centre (NCN), Poland grant no. 2022/47/O/ST1/03299. For the purpose of Open Access, the author has applied a CC-BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.
  • Communicated by: Katrin Gelfert
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3509-3520
  • MSC (2020): Primary 37B10, 37B51; Secondary 37B25, 37B65
  • DOI: https://doi.org/10.1090/proc/16831
  • MathSciNet review: 4767280