Geodesic
A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 29-54 
N. Gherstega; V. Orlov; N. Vulpe. A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2009), pp. 29-54. http://geodesic.mathdoc.fr/item/BASM_2009_2_a2/
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     title = {A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this article we consider the action of the group $Aff(2,\mathbb R)$ of affine transformations and time rescaling on real planar quadratic differential systems. Via affine invariant conditions we give a complete stratification of this family of systems according to the dimension $\mathcal D$ of affine orbits proving that $3\le\mathcal D\le6$. Moreover we give a complete topological classification of all the systems located on the orbits of dimension $\mathcal D\le5$ constructing the affine invariant criteria for the realization of each of 49 possible topologically distinct phase portraits.

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