发表机构
Universidad de Chile（智利大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过构造伪Toeplitz子移位，在任意强轨道等价类中实现了对拓扑熵和因子复杂性的精确控制，从而推广了Sugisaki的结果，并证明了任何Choquet单纯形可作为具有可控复杂性的Toeplitz子移位的测度集。
AI 中文摘要
我们发展了一种方法，用于在任意强轨道等价（SOE）类中构造具有因子复杂性预设上界的最小子移位。这实现了在任意SOE类中拓扑熵的取现，加强了Sugisaki的一系列经典结果。虽然先前的工作建立了零熵系统的复杂性控制，但本工作的方法扩展到了正熵情形。我们的构造引入了伪Toeplitz子移位类，并证明它们存在于任意SOE类中。更精确地说，对于任意$\alpha\geq 1$和以速率$\log(\alpha)$指数增长的序列$g_n$，我们构造了该类中的一个系统，其拓扑熵为$\log(\alpha)$，且其复杂性增长严格快于，或在某些条件下慢于$g_n$。作为推论，任何Choquet单纯形都可以实现为具有精确控制复杂性的Toeplitz子移位的不变测度集，无论是在零熵还是正熵情形下。
英文摘要
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.
Comments29 pages
