Perturbations of multidimensional shifts of finite type

In this paper, we study perturbations of multidimensional shifts of finite type. Specifically, for any Z(d) shift of finite type X with d > 1 and any finite pattern w in the language of X, we denote by X-w the set of elements of X not containing w. For strongly irreducible X and patterns w with shape a d-dimensional cube, we obtain upper and lower bounds on h(top) (X) - h(top) (X-w) dependent on the size of w. This extends a result of Lind for d = 1. We also apply our methods to an undecidability question in Zd symbolic dynamics.