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Journal of Mathematics
Volume 2013, Article ID 404626, 6 pages
http://dx.doi.org/10.1155/2013/404626
Research Article

The Measure-Theoretic Entropy and Topological Entropy of Actions over

1Department of Applied Mathematics, Feng Chia University, Taichung 40724, Taiwan
2Taipei Municipal Minsheng Junior High School, Taipei 10591, Taiwan

Received 31 January 2013; Accepted 29 May 2013

Academic Editor: Mike Tsionas

Copyright © 2013 Chih-Hung Chang and Yu-Wen Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.