We prove a reduction of singularities for pairs of foliations by blowing-up, and then investigate the analytic classification of the reduced models. Those reduced pairs of regular foliations are well understood. The case of a regular and a singular foliation is dealt with Mattei-Moussu's Theorem for which we provide a new proof, avoiding Gronwall's inequality. We end-up announcing results recently obtained by the first author in the case of a pair of reduced foliations sharing the same separatrices.

中文翻译：

---

叶对对和 Mattei-Moussu 定理

我们通过吹胀证明了成对叶片的奇点减少，然后研究了减少模型的分析分类。那些减少的规则叶对是很好理解的。使用 Mattei-Moussu 定理处理规则和奇异叶理的情况，我们为此提供了新的证明，避免了 Gronwall 不等式。我们最终宣布了第一作者最近在一对减少的叶面共享相同分离度的情况下获得的结果。