Upper bound of the directional entropy of a 2-action

摘要

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 ~Z_pκ. 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)].