Recognition and classification for \(O(n)\)-equivariant bifurcations with \(O(n)\)-codimension less than 5
type: Item
instance of: scholarly article
title: Recognition and classification for \(O(n)\)-equivariant bifurcations with \(O(n)\)-codimension less than 5
zbMATH Open document ID: 0917.58007
author: Yun Tang
author: Duo Wang
author: Xiao-Feng Wang
published in: Chinese Annals of Mathematics. Series B
publication date: 1999-08-05T00:00:00Z
review text: This article deals with the local bifurcation problem for the equation \[ g(x,\lambda)=0\;(g:\mathbb{R}^n\times \mathbb{R}\to\mathbb{R}^n) \] under the assumption that \[ g(\gamma x, \lambda)= \gamma g(x,\lambda)\;(\gamma\in \mathbb{O}(n), x\in\mathbb{R}^n, \lambda\in\mathbb{R}). \] The basic result is the complete description of the normal forms and universal unfolding for all 19 possible classes for the bifurcation phenomenon of the equation given above in the case \(\text{codim}_{O (n)}g\leq 4\). Moreover, for all 19 classes the corresponding recognizing conditions are presented.
Mathematics Subject Classification ID: 58E09
zbMATH DE Number: 1229537
zbMATH Keywords: bifurcation problem
zbMATH Keywords: normal forms
zbMATH Keywords: universal unfolding
reviewed by: Peter P. Zabreĭko
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1229537