Analytic normal forms for planar resonant saddle vector fields - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... (Preprint) Year :

Analytic normal forms for planar resonant saddle vector fields

(1)
1

Abstract

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.
Fichier principal
Vignette du fichier
analytic_normal_forms_resonant.pdf (467.51 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03887570 , version 1 (07-12-2022)

Licence

Attribution - NonCommercial - CC BY 4.0

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook Twitter LinkedIn More