Perturbing Subshifts of Finite Type

Nick Ramsey

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arXiv · 2201.05656

Perturbing Subshifts of Finite Type

Nick Ramsey

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Abstract

Given an SFT $\Sigma$ and a finite set $S$ of finite words, let $\Sigma\langle S\rangle$ denote the subshift of $\Sigma$ that avoids $S$. We establish a general criterion under which we can bound the entropy perturbation $h(\Sigma)-h(\Sigma\langle S\rangle)$ 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 $S_i$.

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Nick Ramsey. 2022-01-14. Perturbing Subshifts of Finite Type. https://arxiv.org/abs/2201.05656

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