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PreprintCC BY-NC-ND 4.0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{wu2026generating,
  title = {{Generating Forbidden Words and Measures of Maximal Entropy for Subshifts}},
  author = {Xinxing Wu and Xu Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03758},
  eprint = {2611.03758},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03758},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Generating Forbidden Words and Measures of Maximal Entropy for Subshifts
AU  - Xinxing Wu
AU  - Xu Zhang
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03758
UR  - https://arxiv.org/abs/2611.03758
AB  - 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.
ER  -