Abstract:

In this lecture we shall describe the origin and evolution of ideas on affine and topological invariants and their interaction in problems of classification of planar polynomial differential systems. We shall illustrate the ideas on the test bed of specific classes of quadratic differential systems as well as on the global problem of classifying all possible configurations of finite and infinite singularities occurring in the quadratic class. This last part is work in progress together with Artes, Llibre and Vulpe.