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arXiv · 2611.03758

Generating Forbidden Words and Measures of Maximal Entropy for Subshifts

Xinxing Wu·Xu Zhang
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Abstract

We prove that if the entropy of generating forbidden words of a subshift over a finite alphabet is strictly smaller than its topological entropy, then the subshift has only finitely many ergodic measures of maximal entropy, each of which is Bernoulli up to a finite period, and admits a characteristic measure of maximal entropy. In particular, these conclusions hold when the entropy of minimal forbidden words is strictly smaller than the topological entropy, giving a negative answer to a question of Buzzi.

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Xinxing Wu, Xu Zhang. 2026-11-02. Generating Forbidden Words and Measures of Maximal Entropy for Subshifts. https://arxiv.org/abs/2611.03758

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