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Entropy and complexity in a strong orbit equivalence class via pseudo-Toeplitz subshifts

  • Paulina Cecchi-Bernales
  • Sebastián Donoso
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Abstract

We develop a method for constructing minimal subshifts with a prescribed bound on the factor complexity within any strong orbit equivalence (SOE) class. This implies realizations of topological entropies within any SOE class, strengthening a series of classical results by Sugisaki. While prior work established complexity controls for zero-entropy systems, the approach of the present work extends to positive-entropy regimes. Our construction introduces the class of pseudo-Toeplitz subshifts, and we show that they exist in any SOE class. More precisely, for any α≥ 1 and sequence gn growing exponentially at rate log(α), we construct a system in this class whose topological entropy is log(α) and whose complexity grows strictly faster, or, under certain conditions, slower than gn. As a consequence, any Choquet simplex can be realized as the set of invariant measures of a Toeplitz subshift with precisely controlled complexity, in either a zero or positive-entropy regime.

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Cite

BibTeXRIS
BibTeX
@misc{cecchibernales2026entropy,
  title = {{Entropy and complexity in a strong orbit equivalence class via pseudo-Toeplitz subshifts}},
  author = {Paulina Cecchi-Bernales and Sebastián Donoso},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27313},
  eprint = {2609.27313},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27313},
}
RIS
TY  - UNPB
TI  - Entropy and complexity in a strong orbit equivalence class via pseudo-Toeplitz subshifts
AU  - Paulina Cecchi-Bernales
AU  - Sebastián Donoso
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27313
UR  - https://arxiv.org/abs/2609.27313
AB  - We develop a method for constructing minimal subshifts with a prescribed bound on the factor complexity within any strong orbit equivalence (SOE) class. This implies realizations of topological entropies within any SOE class, strengthening a series of classical results by Sugisaki. While prior work established complexity controls for zero-entropy systems, the approach of the present work extends to positive-entropy regimes. Our construction introduces the class of pseudo-Toeplitz subshifts, and we show that they exist in any SOE class. More precisely, for any α≥ 1 and sequence g_n growing exponentially at rate log(α), we construct a system in this class whose topological entropy is log(α) and whose complexity grows strictly faster, or, under certain conditions, slower than g_n. As a consequence, any Choquet simplex can be realized as the set of invariant measures of a Toeplitz subshift with precisely controlled complexity, in either a zero or positive-entropy regime.
ER  -