One-dimensional projective subdynamics of uniformly mixing Z(d) shifts of finite type

Abstract

We investigate under which circumstances the projective subdynamics of multidimensional shifts of finite type can be non-sofic. In particular, we give a sufficient condition ensuring the one-dimensional projective subdynamics of such Z(d) systems to be sofic and we show that this condition is already met (along certain, respectively all, sublattices) by most of the commonly used uniform mixing conditions. (Examples of the different situations are given.) Complementary to this we are able to prove a characterization of one-dimensional projective subdynamics for strongly irreducible Z(d) shifts of finite type for every d >= 2: in this setting the class of possible subdynamics coincides exactly with the class of mixing Z sofics. This stands in stark contrast to the much more diverse situation in merely topologically mixing multidimensional shifts of finite type.