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Upper Bound Of The Directional Entropy Of A ℤ2-Action

Author

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  • HASAN AKIN

    (Faculty of Education, Zirve University, 27260 Gaziantep, Turkey)

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)].

Suggested Citation

  • Hasan Akin, 2011. "Upper Bound Of The Directional Entropy Of A ℤ2-Action," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 711-718.
    • Handle: RePEc:wsi:ijmpcx:v:22:y:2011:i:07:n:s0129183111016555
    DOI: 10.1142/S0129183111016555
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