Perturbing Subshifts of Finite Type

Abstract

Given an SFT $\Sigma$ and a finite set $S$ of finite words, let $\Sigma ⟨S⟩$ denote the subshift of $\Sigma$ that avoids $S$. We establish a general criterion under which we can bound the entropy perturbation $h(\Sigma )-h(\Sigma ⟨S⟩)$ from above. As an application, we prove that this entropy difference tends to zero with a sequence of such sets $S_1,S_2,\dots$ under various assumptions on the $S_i$.