Scrambled sets in shift spaces on a countable alphabet
edge-shifts on an infinite graph (the subshift of finite type case) or as on an infinite graph (the sofic shift case). We show in the setting of a subshift of finite type on a shift over a countable alphabet that the shift space has Li-Yorke chaos if, and only if, it has a single scrambled pair, and...
Gespeichert in:
Veröffentlicht in: | Proceedings of the American Mathematical Society 2016-01, Vol.144 (1), p.217-224 |
---|---|
Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | edge-shifts on an infinite graph (the subshift of finite type case) or as on an infinite graph (the sofic shift case). We show in the setting of a subshift of finite type on a shift over a countable alphabet that the shift space has Li-Yorke chaos if, and only if, it has a single scrambled pair, and in this case the scrambled set is closed and perfect (but not necessarily compact). We give an example of a sofic shift over an infinite alphabet which has a single scrambled pair but does not have Li-Yorke chaos.]]> |
---|---|
ISSN: | 0002-9939 1088-6826 |
DOI: | 10.1090/proc/12690 |