On directional entropy functions

Given a Z(2)-process, the measure theoretic directional entropy function, h (<(upsilon)over right arrow>), is defined on S-1 = {<(upsilon)over right ar row> : parallel to<(upsilon)over right arrow>parallel to = 1} subset of R-2 . We relate the directional entropy of a Z(2)-process to its R-2 suspension . We find a sufficient condition for the continuity of directional entropy function. In particular, this shows that the directional entropy is continu ous for a Z(2)-action generated by a cellular automaton; this finally answe rs a question of Milnor [Mi1]. We show that the unit vectors whose directio nal entropy is zero form a G(delta) subset of S-1. We study examples to inv estigate some properties of directional entropy functions.