Projectional Entropy In Higher Dimensional Shifts Of Finite Type

Document Type


Publication Date


Published In

Complex Systems


Any higher dimensional shift space (X, ℤᵈ) contains many lower dimensional shift spaces obtained by projection onto r-dimensional sublattices L of ℤᵈ where r < d. We show here that any projectional entropy is bounded below by the ℤᵈ entropy and, in the case of certain shifts of finite type satisfying a mixing condition, equality is achieved if and only if the shift of finite type is the infinite product of a lower dimensional projection.