On the topological directional entropy

In this paper we study the topological directional entropy of Z2-actions generated by one-dimensional linear cellular automata and the shift map σ acting on compact metric space ZmZ. We give a formula, which can be efficiently and rightly computed by means of the coefficients of the local rule f, for the topological directional entropy of Z2-action generated by the pair (Tf[−r,r],σ) in the direction θ (θ∈[0,π]). We also generalize the results obtained by Akın [H. Akin, The topological entropy of invertible cellular automata, J. Comput. Appl. Math. 213 (2) (2008) 501-508] to the topological entropy of any invertible one-dimensional linear cellular automata.