Two parameter families of binary differential equations
type: Item
instance of: scholarly article
title: Two parameter families of binary differential equations
zbMATH Open document ID: 1159.34026
author: Farid Tari
published in: Discrete and Continuous Dynamical Systems
publication date: 2008-11-06T00:00:00Z
review text: The author studies the topological classification of singularities of local codimension \(2\) of binary differential equations of the form \(ady^2+2bdxdy+cdx^2=0\) with smooth coefficients \(a\), \(b\), \(c\) in the case that all coefficients vanish at the singularity. The topological models are obtained by an extension of Guíñez' blowing up technique. It is shown that three different classes exist and for each class a local normal form of the singularity itself and of the corresponding generic two-parameter family arising in bifurcation.
reviewed by: Werner M. Seiler
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 5362918
zbMATH Keywords: binary differential equation
zbMATH Keywords: bifurcation
zbMATH Keywords: generic family
zbMATH Keywords: singularity
zbMATH Keywords: topological equivalence
MaRDI profile type: Publication
full work available at URL: dcds.2008.22.759
OpenAlex ID: W2316127656
DOI: 10.3934/DCDS.2008.22.759
description: scientific article; zbMATH DE number 5362918