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arXiv 2602.040972026-02-04math.DS

子移位的稳定性覆盖

Stable covers of subshifts

Solly Coles, Van Cyr, Bryna Kra, Ronnie Pavlov

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AI总结：

本文研究子移位的稳定性覆盖，通过熵衰减和周期点两种方式证明其稳定化，并展示产生特征测度的机制。

摘要：

给定一个动力系统，特征测度是一个不变于其所有自同构的Borel概率测度。Frisch和Tamuz问是否每个符号系统都支持这样的测度。受此问题启发，我们研究子移位通过其有限型近似所自然覆盖，并探讨这种覆盖在两种意义上可以被说稳定下来。第一种是通过熵衰减，第二种是通过周期点。我们证明第一种稳定化给出了语言稳定的移位类的新特征，并展示了产生特征测度的机制仅依赖于熵差。对于第二种稳定化，我们证明这定义了一类新的子移位，这些移位在共轭下不变，并具有特征测度。

英文摘要：

Given a dynamical system, a characteristic measure is a Borel probability measure invariant under all of its automorphisms. Frisch and Tamuz asked if every symbolic system supports such a measure. Motivated by this problem, we study the natural cover of a subshift by its shift of finite type approximations and two senses in which this cover can be said to stabilize. The first is in terms of entropy decay and the second in terms of periodic points. We show that the first type of stabilization gives a new characterization of the class of language stable shifts and demonstrates that there is a mechanism for producing a characteristic measures that relies only on entropy differences. For the second type of stabilization, we show that this defines a new class of subshifts, invariant under conjugacies, that have characteristic measures.

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