On families \(\boldsymbol{QSL}_{\geq 2}\) of quadratic systems with invariant lines of total multiplicity at least 2
type: Item
instance of: scholarly article
title: On families \(\boldsymbol{QSL}_{\geq 2}\) of quadratic systems with invariant lines of total multiplicity at least 2
author: Cristina Bujac
author: Nicolae Vulpe
author: Dana Schlomiuk
published in: Qualitative Theory of Dynamical Systems
publication date: 2022-10-07T00:00:00Z
review text: The core of authors of this paper has developed along the last years a series of papers on quadratic systems having several invariant lines. They started with systems with 5 or 6 invariant straight lines, and have later gone to more generic situations with less invariant straight lines. It is worth to say that one of the lines considered is always the line at infinity, so the more generic case with just 2 lines means that there is just one affine invariant straight line. It is also worth to mention that when counting the number of invariant lines, they take into account theis multiplicity. Along these years they have produced dual papers, first a paper with a scheme of the possible configurations of invariant lines, and later a paper with the realizable phase portraits. The last cases considered were in the family with 3 invariant straight lines which they had to split in several papers. This is the last of them in which they cover the remaining cases which are those with two parallel invariant straight lines (real or complex) intersecting at an infinite singularity. In this paper they conclude that there are up to 111 different configurations of invariant lines in this class. Now I am eager to see the next paper which should be the realization of phase portraits in this family.
reviewed by: Joan C. Artés
Mathematics Subject Classification ID: 34C45
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 34C05
zbMATH DE Number: 7597829
zbMATH Keywords: quadratic differential system
zbMATH Keywords: invariant line
zbMATH Keywords: singularity
zbMATH Keywords: configuration of invariant lines
zbMATH Keywords: group action
zbMATH Keywords: polynomial invariant
MaRDI profile type: Publication
full work available at URL: s12346-022-00659-x
OpenAlex ID: W4297199277
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DOI: 10.1007/S12346-022-00659-X
description: scientific article; zbMATH DE number 7597829