1:2 resonance for reversible vector fields
type: Item
instance of: scholarly article
title: 1:2 resonance for reversible vector fields
zbMATH Open document ID: 1012.34031
DOI: 10.1016/S1631-073X(02)02169-6
author: Matthieu Barrandon
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2002-08-04T00:00:00Z
review text: The author deals with the \(1:2\) resonance for reversible vector fields in \(\mathbb{R}^4\) depending on a parameter \(\mu: dX/dt= F(X,\mu),\) where \(F\) is in \(C^k\), \(F(0,\mu)=0\) and \(D_X F(0,0)\) has two pairs of simple eigenvalues \(+ i\omega_1, -i\omega_1, +i\omega_2\) and \(-i\omega_2\), and there exists a symmetry \(S\) such that \(SF(X,\mu)=-F(SX,\mu)\).
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 37G15
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37C80
zbMATH DE Number: 1744391
zbMATH Keywords: bifurcation
zbMATH Keywords: reversible vector fields
zbMATH Keywords: periodic solutions
zbMATH Keywords: symmetries
MaRDI profile type: Publication
cites work: A multiplicity of localized buckling modes for twisted rod equations
cites work: Reversible Diffeomorphisms and Flows
cites work: Q4440482
cites work: Q4266071
cites work: Classification and unfoldings of \(1:2\) resonant Hopf bifurcation
description: scientific article; zbMATH DE number 1744391