Abstract

In this lecture we present results on the class of planar quadratic vector fields with invariant straight lines with total multiplicity at least four. We show that all the systems in this class are integrable having either Darboux or more general Liouvillian first integrals. We give bifurcation diagrams and construct moduli spaces with respect to the action of the group of affine transformations and time homotheties for this class of systems.