Abstract
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.
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