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Mean equicontinuity and mean sensitivity on cellular automata

Part of: Topological dynamics

Published online by Cambridge University Press:  03 November 2020

LUGUIS DE LOS SANTOS BAÑOS  and
FELIPE GARCÍA-RAMOS
LUGUIS DE LOS SANTOS BAÑOS
Affiliation:
Instituto de Física, Universidad Autónoma de San Luis Potosí, Av. Dr. Manuel Nava 6, 78290San Luis, SLP, Mexico (e-mail: luguis.sb.25@gmail.com)
FELIPE GARCÍA-RAMOS*
Affiliation:
Instituto de Física, Universidad Autónoma de San Luis Potosí, Av. Dr. Manuel Nava 6, 78290San Luis, SLP, Mexico (e-mail: luguis.sb.25@gmail.com) CONACyT, Mexico City, Mexico
*
e-mail: fgramos@conacyt.mx
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Abstract

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.

Keywords

cellular automatamean equicontinuitymean sensitivityalmost equicontinuityalmost mean equicontinuity

MSC classification

Primary: 37B05: Transformations and group actions with special properties (minimality, distality, proximality, etc.) 37B10: Symbolic dynamics 37B15: Cellular automata
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 41 , Issue 12 , December 2021 , pp. 3704 - 3721
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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