Mean equicontinuity and mean sensitivity on cellular automata

Mean equicontinuity and mean sensitivity on cellular automata

We show that a cellular automaton (or shift-endomorphism) on a transitive subshift is either almost equicontinuous or sensitive. On the other hand, we construct a cellular automaton on a full shift (hence a transitive subshift) that is neither almost mean equicontinuous nor mean sensitive.

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Veröffentlicht in:Ergodic theory and dynamical systems 2021-12, Vol.41 (12), p.3704-3721
Hauptverfasser: DE LOS SANTOS BAÑOS, LUGUIS, GARCÍA-RAMOS, FELIPE
Format: Artikel
Sprache:eng
Schlagworte:
Cellular automata
Dynamical systems
Original Article
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Zusammenfassung:We show that a cellular automaton (or shift-endomorphism) on a transitive subshift is either almost equicontinuous or sensitive. On the other hand, we construct a cellular automaton on a full shift (hence a transitive subshift) that is neither almost mean equicontinuous nor mean sensitive.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2020.108