UPPER BOUND OF THE DIRECTIONAL ENTROPY OF A Z(2)-ACTION
In this short paper, we study the measure directional entropy of a Z(2)-action generated by an invertible one-dimensional linear cellular automaton and the shift map acting on the compact metric space Z(pk)(Z). We obtain an upper bound of the measure directional entropy of the Z(2)-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)].
directional entropy bernoulli measure cellular automata