Quadratic Differential Systems on $\mathbb{R}^{3}$ Having a Semisimple Derivation

Abstract

The classification, up to a center-affinity, of the homogeneous quadratic differential systems defined on $\mathbb{R}^{3}$ that have at least a semisimple nonsingular derivation, is achieved. It is proved that there exist four affine-equivalence classes of such systems, only.