Versal unfolding for rank-2 singularities of positive quadratic differential forms: The remaining case
type: Item
instance of: scholarly article
title: Versal unfolding for rank-2 singularities of positive quadratic differential forms: The remaining case
zbMATH Open document ID: 1080.58026
author: Víctor Guíñez
author: Eduardo Sáez
published in: Discrete and Continuous Dynamical Systems
publication date: 2005-06-21T00:00:00Z
review text: Authors study rank-2 singular points of positive quadratic differential forms (in local coordinates) \[ \omega = a(x,y)dy^2+2b(x,y)dxdy+c(x,y)dy^2 \] on oriented two-dimensional manifolds. To each positive quadratic differential form \(\omega \) defined on an oriented two-dimensional manifold they associate two transversal one-dimensional foliations with common set of singular points. The three different locally stable phase portraits and their normal forms, associated to these foliations around the singularity are obtained and the versal unfoldings of the normal forms are constructed and the respective codimensions are calculated. Using the blowing up techniques the case of rank-2 singular points with the parametrized form of singularity denoted by \(E(\lambda )\) is investigated in relatively complete form with finding a normal form of any family of positive quadratic differential forms by analytic change of coordinates and singularity type \(E(\lambda )\) at zero of parameter value.
reviewed by: Stanisław Janeczko
Mathematics Subject Classification ID: 58K45
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 37G10
zbMATH DE Number: 2177528
zbMATH Keywords: singularities
zbMATH Keywords: quadratic forms
zbMATH Keywords: differential forms
zbMATH Keywords: normal forms
MaRDI profile type: Publication
full work available at URL: dcds.2005.12.887
OpenAlex ID: W1971556174
DOI: 10.3934/DCDS.2005.12.887
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description: scientific article; zbMATH DE number 2177528