This paper contains theory on two related topics relevant to manifolds of normally hyperbolic singularities. First, theorems on the formal and \( C^k \) normal forms for these objects are proved. Then, the theorems are applied to give asymptotic properties of the transition map between sections transverse to the centre-stable and centre-unstable manifolds of some normally hyperbolic manifolds. A method is given for explicitly computing these so called Dulac maps. The Dulac map is revealed to have similar asymptotic structures as in the case of a saddle singularity in the plane.

中文翻译：

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常双曲奇异性的流形的范式和附近过渡的渐近性质

本文包含有关与正常双曲奇点的流形相关的两个相关主题的理论。首先，证明了这些对象的形式形式和\（C ^ k \）范式定理。然后，应用定理给出横切某些正常双曲流形的中心稳定歧管和中心不稳定歧管的截面之间的过渡图的渐近性质。给出了一种显式计算这些所谓的Dulac映射的方法。与平面上的鞍形奇异点相比，Dulac映射具有类似的渐近结构。