Geodesic
Complete geometric invariant study of two classes of quadratic systems
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     title = {Complete geometric invariant study of two classes of quadratic systems},
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     volume = {2012},
     year = {2012},
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     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/