On strong mixing property of cellular automata with respect to Markov measures
نویسنده
چکیده
In this paper we study mixing properties of one-dimensional linear cellular automata over the ring Zm, a particular class of dynamical systems, determined by right (left) permutative local rule F with respect to the uniform Markov measure induced by doubly stochastic matrix P = p(i,j) and the probability vector π. We prove that one-dimensional linear cellular automata associated to right (resp. left) permutative local rule F = F [l, r], 0 < l < r (resp. l < r < 0), is strong mixing with respect to the uniform Markov measure. We also show that Z×N-actions generated by the one-dimensional linear cellular automata determined by bipermutative local rule F = F [l, r] and shift map is strong mixing with respect to the uniform Markov measure. 2010 Mathematics Subject Classification: Primary 28D20; Secondary 37B15, 37A05.
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