Analytic normal forms for convergent saddle-node vector fields

Reinhard Schäfke (1) , Loïc Teyssier (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We give unique analytic "normal forms" for germs of a holomorphic vector field of the complex plane in the neighborhood of an isolated singularity of saddle-node type having a convergent formal separatrix. We specifically address the problem of computing the normal form explicitly.

Mots clés: analytic vector fields; normal forms; singularities; effective methods in differential equations

Domaines: Systèmes dynamiques [math.DS]

Reinhard Schäfke, Loïc Teyssier. Analytic normal forms for convergent saddle-node vector fields. Annales de l'Institut Fourier, 2015, 65 (3), pp.933--974. ⟨hal-00843190v2⟩