Further reduction of the Takens-Bogdanov normal form
type: Item
instance of: scholarly article
title: Further reduction of the Takens-Bogdanov normal form
zbMATH Open document ID: 0761.34027
DOI: 10.1016/0022-0396(92)90022-F
author: Alberto Baider
author: Jan A. Sanders
published in: Journal of Differential Equations
publication date: 1993-01-16T00:00:00Z
review text: Normal forms (analytic or formal) play an important role in the theory of systems of ODE, solving birfurcation or stability type problems. The idea of normalisation is the elimination of as many as possible terms. The authors formulate and prove a unique formal classification of analytic vector fields in \(R^ 2\) with nilpotent linear part. The investigation is divided in three subcases and except one subcase it is essentially complete. The paper has a high theoretical level, it applies the technics of Lie-algebras.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 93316
zbMATH Keywords: normal forms
zbMATH Keywords: birfurcation
zbMATH Keywords: normalisation
zbMATH Keywords: unique formal classification of analytic vector fields in \(R^ 2\) with nilpotent linear part
zbMATH Keywords: Lie- algebras
reviewed by: Péter F. Moson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 93316