Perturbing Subshifts of Finite Type

2022/01/14 by Nick Ramsey, Ramsey, Nick
Mathematics · #37B10 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37B10

paper · pdf · doi:10.48550/arxiv.2201.05656

arxiv created 2022/01/14 · arxiv updated 2022/01/19

Abstract

Given an SFT Σ and a finite set S of finite words, let Σ⟨ S⟩ denote the subshift of Σ that avoids S. We establish a general criterion under which we can bound the entropy perturbation h(Σ)-h(Σ⟨ S⟩) from above. As an application, we prove that this entropy difference tends to zero with a sequence of such sets S₁, S₂, … under various assumptions on the S_i.

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