Reversibility and classification of nilpotent centers
type: Item
instance of: scholarly article
title: Reversibility and classification of nilpotent centers
zbMATH Open document ID: 0803.34005
publication date: 1995-01-03T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/75070
review text: We consider a germ \(\omega\) of analytic 1-form in \(\mathbb{R}^ 2\), 0 with 1- jet \(ydy\). We prove that if \(\omega= 0\) defines a center (i.e. all solutions are cycles) there exists an analytic involution of \(\mathbb{R}^ 2\), 0 preserving the phase portrait of the system. Geometrically this means that analytic nilpotent centers are built by pull back with fold applications. A theorem of equivariant conjugacy leads to the complete classification of such centers.
Mathematics Subject Classification ID: 34A25
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A99
Mathematics Subject Classification ID: 32G34
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 672149
zbMATH Keywords: center
zbMATH Keywords: analytic involution
zbMATH Keywords: phase portrait
zbMATH Keywords: equivariant conjugacy
zbMATH Keywords: classification
author: Michel Berthier
author: Robert Moussu
MaRDI profile type: Publication
OpenAlex ID: W1970014790
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DOI: 10.5802/AIF.1406
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published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 672149