Based on our previous graph covering method, we introduce weighted graph covering models and flexible graph covering models that are almost equivalent to the well-known Bratteli--Vershik models. These models play important roles in showing that every invertible dynamical system on compact metrizable zero-dimensional space admits a non-trivial Bratteli--Vershik model and a basic set. We can also obtain an analogue of Krieger's lemma for compact metrizable zero-dimensional systems. The flexible graph covering models enable us to consider "stationary" graph covering models, by which some portion of the substitution subshifts can be expressed. As an application, we show a way of constructing some class of transitive substitution subshifts.

中文翻译：

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Bratteli–Vershik 模型和图覆盖模型

在我们之前的图覆盖方法的基础上，我们引入了加权图覆盖模型和灵活的图覆盖模型，它们几乎等同于众所周知的 Bratteli--Vershik 模型。这些模型在表明紧凑可度量零维空间上的每个可逆动力系统都承认一个非平凡的 Bratteli-Vershik 模型和一个基本集方面发挥了重要作用。我们还可以获得紧凑可计量零维系统的克里格引理的类似物。灵活的图覆盖模型使我们能够考虑“静止”图覆盖模型，通过该模型可以表达某些部分的替代子移位。作为一个应用，我们展示了一种构造一些传递替代子移位的方法。