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 G_δ subset of an appropriate subspace. We identify the odometer in several cases.

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About

• Item ORO ID
• 67101
• Item Type
• Journal Item
• ISSN
• 1088-6826
• Keywords
• Odometer; cellular automaton
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2006 American Mathematical Society
• Depositing User
• Reem Yassawi