Based on previous work of the authors, to any S-adic development of a subshift X a ‘directive sequence’ of commutative diagrams is associated, which consists at every level $n \geq 0$ of the measure cone and the letter frequency cone of the level subshift $X_n$ associated canonically to the given S-adic development. The issuing rich picture enables one to deduce results about X with unexpected directness. For instance, we exhibit a large class of minimal subshifts with entropy zero that all have infinitely many ergodic probability measures. As a side result, we also exhibit, for any integer $d \geq 2$ , an S-adic development of a minimal, aperiodic, uniquely ergodic subshift X, where all level alphabets $\mathcal A_n$ have cardinality $d,$ while none of the $d-2$ bottom level morphisms is recognizable in its level subshift $X_n \subseteq \mathcal A_n^{\mathbb {Z}}$ .

中文翻译：

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测量换档的转移和 S-adic 发展

根据作者之前的工作，对于任何S- 子变速的快速发展X交换图的“指令序列”是相关联的，它包含在每个级别 $n \geq 0$ 测量锥体和水平子移的字母频率锥体 $X_n$ 规范地关联到给定的S- 快速发展。发布丰富的图片可以推断出有关的结果X出人意料的直接。例如，我们展示了一类熵为零的最小子平移，它们都具有无限多个遍历概率度量。作为附带结果，我们还展示了对于任何整数 $d \geq 2$ ， 一个S-最小的、非周期性的、独特的遍历子移的adic发展X，其中所有级别的字母表 $\数学A_n$ 有基数 $d,$ 虽然没有一个 $d-2$ 底层态射在其能级子移中是可识别的 $X_n \subseteq \mathcal A_n^{\mathbb {Z}}$ 。