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arXiv · 2106.09641

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

Luguis de los Santos Baños·Felipe García-Ramos
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Abstract

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.

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Luguis de los Santos Baños, Felipe García-Ramos. 2021-06-17. Local non-periodic order and diam-mean equicontinuity on cellular automata. https://doi.org/10.1080/14689367.2022.2106823

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