论文标题
$ \ MATHCAL {S} $的动力和熵 - 图形移动
Dynamics and entropy of $\mathcal{S}$-graph shifts
论文作者
论文摘要
$ s $ gap班次是一类精心研究的轮班空间，这导致了一些拟议的概括。本文介绍了一个新的偏移空间，称为$ \ mathcal {s} $ - 图形移动，其基本结构以新颖的方式编码，作为有限的有针对的图形，其中一组自然数分配给了每个顶点。 $ \ MATHCAL {S} $ - 图形偏移包含$ S $ -GAP偏移及其概括，以及所有顶点偏移和SFT，作为特殊情况，从而提供了一种以均匀方式研究这些变化空间的方法。本文的主要结果是用于任何$ \ MATHCAL {S} $ - 图形移位的熵的公式，通过专业化，它可以解决Matson和Sattler提出的问题。第二个结果建立了$ \ Mathcal {s} $ - 图形移动的Zeta函数的明确公式。此外，我们表明每个熵值都是通过无数$ \ Mathcal {s} $ - 图形移动来获得的。
$S$-gap shifts are a well-studied class of shift spaces, which has led to several proposed generalizations. This paper introduces a new class of shift spaces called $\mathcal{S}$-graph shifts whose essential structure is encoded in a novel way, as a finite directed graph with a set of natural numbers assigned to each vertex. $\mathcal{S}$-graph shifts contain $S$-gap shifts and their generalizations, as well as all vertex shifts and SFTs, as special cases, thereby providing a method to study these shift spaces in a uniform way. The main result in this paper is a formula for the entropy of any $\mathcal{S}$-graph shift, which, by specialization, resolves a problem proposed by Matson and Sattler. A second result establishes an explicit formula for the zeta functions of $\mathcal{S}$-graph shifts. Additionally, we show that every entropy value is obtained by uncountably many $\mathcal{S}$-graph shifts.
