Abstract

We consider the action of the real afine group Aff(2;R) on the class of real planar polynomial differential systems of degree m. We also consider the Lie algebra of the group G of all linear transformations of Rm(m+1) induced by the above action. Applying the operators in this Lie algebra as well as some others, we construct afine invariant polynomials which are responsible for certain geometrical properties of such differential systems. In particular, for the class of quadratic systems we construct afine invariants which govern the behavior of the trajectories around real singularities. Other applications will also be given.