RO  EN
IMI/Publicaţii/BASM/Ediţii/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

Abstract

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
E-mail:

Nicolae Vulpe
Institute of Mathematics and Computer Science
Academy of Science of Moldova
E-mail:

Fulltext

Adobe PDF document0.21 Mb