The Measure-Theoretic Entropy and Topological Entropy of Actions over

Chih-Hung Chang and Yu-Wen Chen

Journal of Mathematics, 2013, vol. 2013, 1-6

Abstract:

This paper studies the quantitative behavior of a class of one-dimensional cellular automata, named weakly permutive cellular automata, acting on the space of all doubly infinite sequences with values in a finite ring , . We calculate the measure-theoretic entropy and the topological entropy of weakly permutive cellular automata with respect to any invariant measure on the space . As an application, it is shown that the uniform Bernoulli measure is the unique maximal measure for linear cellular automata among the Markov measures.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:404626

DOI: 10.1155/2013/404626

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