IMCS/Publications/BASM/Issues/BASM n.2(90), 2019/

The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials

Authors: Dana Schlomiuk, Vulpe Nicolae


In this paper we provide affine invariant necessary and sufficient conditions for a non-degenerate quadratic differential system to have an invariant conic f(x,y) = 0 and a Darboux invariant of the form f(x,y)λest with λ,s ∈ R and s≠0. The family of all such systems has a total of seven topologically distinct phase portraits. For each one of these seven phase portraits we provide necessary and sufficient conditions in terms of affine invariant polynomials for a non-degenerate quadratic system in this family to possess this phase portrait.

Dana Schlomiuk
Département de Mathématiques
et de Statistiques Université de Montréal

Nicolae Vulpe
Institute of Mathematics and Computer Science
Academy of Science of Moldova


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