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The Measure-Theoretic Entropy and Topological Entropy of Actions over

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  • Chih-Hung Chang
  • Yu-Wen Chen

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.

Suggested Citation

  • Chih-Hung Chang & Yu-Wen Chen, 2013. "The Measure-Theoretic Entropy and Topological Entropy of Actions over," Journal of Mathematics, Hindawi, vol. 2013, pages 1-6, June.
    • Handle: RePEc:hin:jjmath:404626
    DOI: 10.1155/2013/404626
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