Abstract:

In this presentation we are going to give a new point of view around singular points of planar differential systems (specially the polynomial ones), which portrays many more properties than the simple topological ones. We will introduce a new and complete notation for them, created to describe any singular point of a polynomial system, regardless of its degree of degeneracy. We will also introduce some new relations of equivalence between singularities needed to construct the geometric equivalence relation which allows a level of distinction unseen until now and which is completely algebraic.

These results come from a joint work with J. Llibre, D. Schlomiuk and N. Vulpe.