Prevalence of odometers in cellular automata

Coven, Ethan M.; Pivato, Marcus and Yassawi, Reem (2007). Prevalence of odometers in cellular automata. Proceedings of the American Mathematical Society, 135(3) pp. 815–821.

DOI: https://doi.org/10.1090/S0002-9939-06-08754-5

Abstract

We consider left permutive cellular automata Φ with no memory and positive anticipation, defined on the space of all doubly infinite sequences with entries from a finite alphabet. For each such automaton that is not one-to-one, there is a dense set of points x such that Φ : cl{Φn(x) : n ≥ 0} → cl{Φn(x) : n ≥ 0} is topologically conjugate to an odometer, the "+1" map on the countable product of finite cyclic groups. This set is a dense Gδ subset of an appropriate subspace. We identify the odometer in several cases.

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