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

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. 
@article{BASM_2009_2_a2,
     author = {N. Gherstega and V. Orlov and N. Vulpe},
     title = {A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {29--54},
     publisher = {mathdoc},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2009_2_a2/}
}
TY  - JOUR
AU  - N. Gherstega
AU  - V. Orlov
AU  - N. Vulpe
TI  - A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2009
SP  - 29
EP  - 54
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BASM_2009_2_a2/
LA  - en
ID  - BASM_2009_2_a2
ER  - 
%0 Journal Article
%A N. Gherstega
%A V. Orlov
%A N. Vulpe
%T A complete classification of quadratic differential systems according to the dimensions of $Aff(2,\mathbb R)$-orbits
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2009
%P 29-54
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BASM_2009_2_a2/
%G en
%F BASM_2009_2_a2
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/