Geodesic
Complete geometric invariant study of two classes of quadratic systems
Electronic journal of differential equations, Tome 2012 (2012)
In this article, using affine invariant conditions, we give a complete study for quadratic systems with center and for quadratic Hamiltonian systems. There are two improvements over the results in [30] that studied centers up to GL-invariant, and over the results in [1] that classified Hamiltonian quadratic systems without invariants. The geometrical affine invariant study presented here is a crucial step toward the goal of the invariant classification of all quadratic systems according to their singularities, finite and infinite.
Classification : 34C05, 34A34
Keywords: quadratic vector fields, weak singularities, type of singularity 
@article{EJDE_2012__2012__a17,
     author = {Artes,  Joan C. and Llibre,  Jaume and Vulpe,  Nicolae},
     title = {Complete geometric invariant study of two classes of quadratic systems},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1243.34044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a17/}
}
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Artes,  Joan C.; Llibre,  Jaume; Vulpe,  Nicolae. Complete geometric invariant study of two classes of quadratic systems. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a17/