Mean equicontinuity and mean sensitivity on cellular automata

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.

arXiv commentto appear in Ergodic theory and dynamical systems

References in corpus (5)

• Mean equicontinuity and mean sensitivity
• Some properties of cellular automata with equicontinuity points
• Bounded complexity, mean equicontinuity and discrete spectrum
• Mean equicontinuity, almost automorphy and regularity
• The structure of mean equicontinuous group actions

Cited by in corpus (2)

• Diameter mean equicontinuity and cellular automata
• Local non-periodic order and diam-mean equicontinuity on cellular automata