UPPER BOUND OF THE DIRECTIONAL ENTROPY OF A ℤ2-ACTION

Hasan Akin ()
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Hasan Akin: Faculty of Education, Zirve University, 27260 Gaziantep, Turkey

International Journal of Modern Physics C (IJMPC), 2011, vol. 22, issue 07, 711-718

Abstract: In this short paper, we study the measure directional entropy of a ℤ2-action generated by an invertible one-dimensional linear cellular automaton and the shift map acting on the compact metric space$\mathbb{Z}^{\mathbb{Z}}_{p^k}$. We obtain an upper bound of the measure directional entropy of the ℤ2-action with respect to arbitrary Bernoulli measures without making use of the natural extension previously used in the paper [M. Courbage and B. Kaminski,Studia Math.153(3), 285–295 (2002)].

Keywords: Cellular automata; directional entropy; Bernoulli measure (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S0129183111016555

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