A characterization of ω-limit sets in subshifts of Baire space

A characterization of ω-limit sets in subshifts of Baire space

In this paper we consider the structure of ω-limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate that many classical structure theorems for ω-limit sets fail in this context. Nevertheless, we obtain characterizations of ω...

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Veröffentlicht in:Journal of mathematical analysis and applications 2021-08, Vol.500 (1), p.125097, Article 125097
Hauptverfasser: Meddaugh, Jonathan, Raines, Brian E.
Format: Artikel
Sprache:eng
Schlagworte:
Baire space
Chain transitivity
Shadowing
Subshifts
ω-Limit sets
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Zusammenfassung:In this paper we consider the structure of ω-limit sets in subshifts of Baire space. We consider both subshifts of finite type and subshifts of bounded type and we demonstrate that many classical structure theorems for ω-limit sets fail in this context. Nevertheless, we obtain characterizations of ω-limit sets in subshifts of finite types and of attracting ω-limit sets in subshifts of bounded type.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125097