Rauzy-type dynamics are group actions on a collection of combinatorial objects. The first and best known example (the Rauzy dynamics) concerns an action on permutations, associated to interval exchange transformations (IET) for the Poincar\'e map on compact orientable translation surfaces. The equivalence classes on the objects induced by the group action have been classified by Kontsevich and Zorich, and by Boissy through methods involving both combinatorics algebraic geometry, topology and dynamical systems. Our first paper proposed an ad hoc combinatorial proof of this classification. In this paper we define a general method, called the labelling method, which allows one to classify Rauzy-type dynamics in a much more systematic way. We apply the method to the Rauzy dynamics and obtain a second combinatorial proof of the classification.

翻译：Rauzy 类型动态是组合对象集合的群集动作。 第一个和最知名的例子( Rauzy 动态) 是关于组合动作的动作, 与紧凑可调整翻译表面的Poincar\'e地图的间交换转换有关。 群集动作引发的物体的等值分类由 Kontsevich 和 Zorich 分类, 由Boissy 分类, 方法涉及组合数代数几何、 地形学和动态系统。 我们的第一篇论文提议对这一分类进行特别的组合验证。 在这份论文中, 我们定义了一种一般方法, 叫做标签法, 允许一种更系统化的方法对劳兹型的动态分类进行分类。 我们用这种方法对劳兹动力进行分类, 并获得该分类的第二个组合验证 。