Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 09, pp. 1-35.

Title: Complete geometric invariant study of two classes of quadratic systems

Authors: Joan C. Artes (Univ. Autonoma de Barcelona,  Spain)
         Jaume Llibre  (Univ. Autonoma de Barcelona,  Spain)
	 Nicolae Vulpe (Academy of Science of Moldova, Chisinau, Moldova)

Abstract:
 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.

Submitted May 16, 2011. Published January 13, 2012.
Math Subject Classifications: 34C05, 34A34.
Key Words: Quadratic vector fields; weak singularities; type of singularity.