Mean dimension of continuous cellular automata

We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit one-dimensional automata. In higher dimensions, a CA permutative algeb...

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Bibliographic Details
Published inIsrael journal of mathematics Vol. 259; no. 1; pp. 311 - 346
Main Authors Burguet, David, Shi, Ruxi
Format Journal Article
LanguageEnglish
Published Jerusalem The Hebrew University Magnes Press 01.03.2024
Springer Nature B.V
Springer
Subjects
Algebra
Analysis
Applications of Mathematics
Cellular automata
Group Theory and Generalizations
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
68Q80
2020 Mathematics Subject Classification. 37B15
54F45
Online AccessGet full text
ISSN0021-2172
1565-8511
DOI10.1007/s11856-023-2493-9

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Summary:We investigate the mean dimension of a cellular automaton (CA for short) with a compact non-discrete space of states. A formula for the mean dimension is established for (near) strongly permutative, permutative algebraic and unit one-dimensional automata. In higher dimensions, a CA permutative algebraic or having a spaceship has infinite mean dimension. However, building on Meyerovitch’s example [Mey08], we give an example of an algebraic surjective cellular automaton with positive finite mean dimension.
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ISSN:0021-2172
1565-8511
DOI:10.1007/s11856-023-2493-9