Analytic normal forms for convergent saddle-node vector fields

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.

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Source ISSN: 0373-0956
Author Schäfke, Reinhard, Teyssier, Loïc
Maintainer CCSD
Last Updated May 10, 2026, 05:14 (UTC)
Created May 10, 2026, 05:14 (UTC)
Identifier hal-00843190
Language en
Rights https://hal.science/licences/copyright/
contributor Institut de Recherche Mathématique Avancée (IRMA) ; Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)
creator Schäfke, Reinhard
date 2015-05-10T00:00:00
harvest_object_id 79c9b54b-9d26-47ce-b650-407dc61e0f88
harvest_source_id 3374d638-d20b-4672-ba96-a23232d55657
harvest_source_title test moissonnage SELUNE
metadata_modified 2025-12-24T00:00:00
relation info:eu-repo/semantics/altIdentifier/arxiv/1307.2840
set_spec type:ART