Bifurcation at infinity in polynomial vector fields
type: Item
instance of: scholarly article
title: Bifurcation at infinity in polynomial vector fields
zbMATH Open document ID: 0778.34024
author: Christiane Rousseau
author: Terence R. Blows
published in: Journal of Differential Equations
publication date: 1993-10-25T00:00:00Z
review text: We study here the appearance of limit cycles from the equator in polynomial vector fields with no singular points at infinity: this bifurcation is a generalized Hopf bifurcation from the point at infinity. We start with the general theory and then specialize to the particular case of cubic polynomial systems for which we study the simultaneous bifurcation of limit cycles from the origin and from the equator. We finally discuss the transformation of a weak focus at infinity into a finite weak focus.
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 431260
zbMATH Keywords: limit cycles
zbMATH Keywords: polynomial vector fields
zbMATH Keywords: generalized Hopf bifurcation from the point at infinity
zbMATH Keywords: weak focus at infinity
reviewed by: Abdelkader Boucherif
MaRDI profile type: Publication
full work available at URL: jdeq.1993.1070
OpenAlex ID: W2076472288
DOI: 10.1006/JDEQ.1993.1070
description: scientific article; zbMATH DE number 431260