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 that studied centers up to GL-invariant, and over the results in 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. © 2012 Texas State University - San Marcos.
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 31 Jan 2012|
- Quadratic vector fields
- Type of singularity
- Weak singularities