Non-uniqueness of measures of maximal entropy for subshifts of finite type
Robert Main Burton, Jeffrey E. Steif · Ergodic Theory and Dynamical Systems · 1994
Abstract It is known that in one dimension an irreducible subshift of finite type has a unique measure of maximal entropy, the so-called Parry measure. Here we give a counterexample to this in higher dimensions. For this example, we also describe the geometric structure of the measures of maximal entropy and show that there are exactly two extremal measures.