Analytic normal forms for planar resonant saddle vector fields

Loïc Teyssier (1)

1 IRMA - Institut de Recherche Mathématique Avancée

We give essentially unique “normal forms” for germs of a holomorphic vector field of the complex plane in the neighborhood of an isolated singularity which is a p:q resonant-saddle. Hence each vector field of that type is conjugate, by a germ of a biholomorphic map at the singularity, to a preferred element of an explicit family of vector fields. These model vector fields are polynomial in the resonant monomial. Abstract. This work is a followup of a similar result obtained for parabolic diffeomorphisms which are tangent to the identity, and solves the long standing problem of finding explicit local analytic models for resonant saddle vector fields.

Mots clés: Normal forms; Holomorphic vector fields; Inverse problem

Domaines: Systèmes dynamiques [math.DS]

Loïc Teyssier. Analytic normal forms for planar resonant saddle vector fields. 2022. ⟨hal-03887570⟩