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

Paulina Cecchi-Bernales; Sebastián Donoso

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arXiv · 2609.27313

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 $α\geq 1$ 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.

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BibTeX RIS

Paulina Cecchi-Bernales, Sebastián Donoso. 2026-09-23. Entropy and complexity in a strong orbit equivalence class via pseudo-Toeplitz subshifts. https://arxiv.org/abs/2609.27313

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