Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (2): 579-592.doi: 10.1016/S0252-9602(16)30022-4

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TOPOLOGICAL ENTROPY OF PERIODIC COVEN CELLULAR AUTOMATA

Weibin LIU, Jihua MA   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2014-11-20 Revised:2015-06-02 Online:2016-04-25 Published:2016-04-25
  • Supported by:

    The first author is supported by the Fundamental Research Funds for the Central Universities (2012201020204), and the second author is supported by NSFC (11171128, 11271148).

Abstract:

We investigate topological entropy of periodic Coven cellular automatas; that is, the maps FB:{0, 1}Z→{0, 1}Z defined by FB(x)i=xi+(xi+j+bj) (mod 2), where B=b1b2br∈{0, 1}r(r≥2), is a periodic word. In particular, we prove that if the minimal period of B is greater than r/2, the topological entropy is log 2.

Key words: Cellular automata, periodic word, topological entropy

CLC Number: 

  • 37B15
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