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

Diam-mean equicontinuity is a dynamical property that has been of use in the study of non-periodic order. Using some type of "local" skew product between a shift and an odometer looking cellular automaton (CA), we will show there exists an almost diam-mean equicontinuous CA that is not almost equicontinuous, (and hence not almost locally periodic). As an application we show that Kurka's dichotomy does not hold for diam-mean versions of sensitivity and equicontinuity.

preprint2022arXivOpen access
Luguis de los Santos BañosFelipe García-Ramos
math.DSnlin.CG
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Luguis de los Santos BañosFelipe García-Ramos

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