Entropy gaps and locally maximal entropy in $\mathbb{Z}^d$ subshifts
Anthony Quas, Ayşe Şahı̇n · Ergodic Theory and Dynamical Systems · 2003
In this paper, we study the behaviour of the entropy function of higher-dimensional shifts of finite type. We construct a topologically mixing shift of finite type X with the property that there is a uniform gap between the topological entropy of X and the topological entropy of any subshift of X with stronger mixing properties. Our examples illustrate the necessity of strong topological mixing hypotheses in existing higher-dimensional representation and embedding theorems.