Geodesic
The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2019), pp. 41-55

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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 $s\ne0$. 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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     author = {Dana Schlomiuk and Nicolae Vulpe},
     title = {The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {41--55},
     publisher = {mathdoc},
     number = {2},
     year = {2019},
     language = {en},
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}
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Dana Schlomiuk; Nicolae Vulpe. The topological classification of a family of quadratic differential systems in terms of affine invariant polynomials. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2019), pp. 41-55. http://geodesic.mathdoc.fr/item/BASM_2019_2_a2/