Subshifts of multi-dimensional shifts of finite type
Anthony Quas, Paul B. Trow · Ergodic Theory and Dynamical Systems · 2000
We show that every shift of finite type $X$ with positive entropy has proper subshifts of finite type with entropy strictly smaller than the entropy of $X$, but with entropy arbitrarily close to the entropy of $X$. Consequently, $X$ contains an infinite chain of subshifts of finite type which is strictly decreasing in entropy.