Classification of Quadratic Differential Systems on $\mathbb{R}^{3}$ Having a Semisimple Derivation with a one-Dimensional Kernel

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 derivation with one-dimensional kernel, is achieved. It is proved that there exist 35 families of affine equivalence classes of such systems.