On families \(\boldsymbol{QSL}_{\geq 2}\) of quadratic systems with invariant lines of total multiplicity at least 2
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.
scientific article; zbMATH DE number 7597829
scientific article