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Preprints, Working Papers, ... (Preprint) Year : 2022

Analytic normal forms for planar resonant saddle vector fields

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.
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Dates and versions

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

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Attribution - NonCommercial

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