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

Dana Schlomiuk ; Nicolae Vulpe

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2019), pp. 41-55.

Résumé

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 $f(x,y{)}^{\lambda }{e}^{st}$ with $\lambda ,s\in \mathbb{R}$ and $s\ne 0$. 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.

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