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
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Previous version: Original version posted June 18, 2024
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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