On the measure entropy of additive cellular automata \(f_\infty\)
type: Item
instance of: scholarly article
title: On the measure entropy of additive cellular automata \(f_\infty\)
zbMATH Open document ID: 1062.37005
author: Hasan Akin
published in: Entropy
publication date: 2005-03-22T00:00:00Z
full work available at URL: e5020233.htm
review text: Summary: We show that for an additive one-dimensional cellular automaton \(f_\infty\) on the space of all doubly infinitive sequences with values in a finite set \(S = \{0, 1, 2,\dots, r-1\}\), determined by an additive automaton rule \(f(x_{n-k},\dots, x_{n+k}) =\sum^k_{i=-k} x_{n+k} (\text{mod } r)\), and an \(f_\infty\) -invariant uniform Bernoulli measure \(\mu\), the measure-theoretic entropy of the additive one-dimensional cellular automaton \(f_\infty\) with respect to \(\mu\) is equal to \(h_\mu (f_\infty) = 2k\log r\), where \(k\geq 1, r-1\in S\) . We also show that the uniform Bernoulli measure is a measure of maximal entropy for additive one-dimensional cellular automata \(f_\infty\).
Mathematics Subject Classification ID: 37B15
Mathematics Subject Classification ID: 37A35
Mathematics Subject Classification ID: 37B40
zbMATH DE Number: 2148942
zbMATH Keywords: cellular automata
zbMATH Keywords: measure-theoretic entropy
zbMATH Keywords: topological entropy
MaRDI profile type: Publication
OpenAlex ID: W2105288051
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DOI: 10.3390/E5020233
description: scientific article; zbMATH DE number 2148942