Factoring higher-dimensional shifts of finite type onto the full shift
Aimee S. A. Johnson, Kathleen Madden · Ergodic Theory and Dynamical Systems · 2005
A one-dimensional shift of finite type $(X, \mathbb Z)$ with entropy at least log n factors onto the full n -shift. The factor map is constructed by exploiting the fact that X , or a subshift of X , is conjugate to a shift of finite type in which every symbol can be followed by at least n symbols. We will investigate analogous statements for higher-dimensional shifts of finite type. We will also show that for a certain class of mixing higher-dimensional shifts of finite type, sufficient entropy implies that $(X,\mathbb Z^d )$ is finitely equivalent to a shift of finite type that maps onto the full n -shift.