On the absence of invariant measures with locally maximal entropy for a class of ℤ^{𝕕} shifts of finite type

Abstract

We prove that for a class of Z d \mathbb Z^d shifts of finite type, d > 1 d>1 , any invariant measure which is not a measure of maximal entropy can be perturbed a small amount in the weak* topology to an invariant measure of higher entropy. Namely, there are no invariant measures which are strictly local maxima for the entropy function.