Complete geometric invariant study of two classes of quadratic systems

• Main Authors: Joan C. Artes, Jaume Llibre, Nicolae Vulpe
• Format: Article
• Language: English
• Published: Texas State University 2012-01-01
• Series: Electronic Journal of Differential Equations
• Subjects: Quadratic vector fields; weak singularities; type of singularity
• Online Access: http://ejde.math.txstate.edu/Volumes/2012/09/abstr.html
• ISSN: 1072-6691

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.