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- W2068204559 abstract "In this short paper, without considering the natural extension we study the directional entropy of a Z 2 -action Φ generated by an invertible one-dimensional linear cellular automaton [Formula: see text] and [Formula: see text], over the ring Z p k (with p a prime number and k ≥ 2), where gcd (p, λ r ) = 1 and p ∣ λ i for all i ≠ r, and the shift map acting on the compact metric space [Formula: see text]. Without loss of generality, we consider k = 2. We prove that the directional entropy h v (Φ)(v = (s, q) ∈ R) of a Z 2 -action with respect to a Markov measure μ πP over space [Formula: see text] defined by a stochastic matrix P = (a ij ) and a probability vector π = {π 0 , π 1 , …, π p 2 -1 } is bounded above by [Formula: see text]." @default.
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- W2068204559 date "2012-11-01" @default.
- W2068204559 modified "2023-09-29" @default.
- W2068204559 title "AN UPPER BOUND OF THE DIRECTIONAL ENTROPY WITH RESPECT TO THE MARKOV MEASURES" @default.
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- W2068204559 doi "https://doi.org/10.1142/s021812741250263x" @default.
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