Abstract

According to results of Zhang Pingguang, the maximum number of limit cycles occurring in quadratic vector fields with a second order weak focus is two. Recent work of Artes, Llibre and Schlomiuk shows that this number can be attained by perturbing within this family the most degenerate quadratic system with a center i.e. the only such system having a line of singularities at infinity. How does this system unfold within the quadratic family? This is clearly a hard problem and a motivation for the work we present in this lecture. In this lecture we construct the moduli space of all quadratic systems with a line of singularities at infinity and give its bifurcation diagram. The proofs use the theory of algebraic invariants.

This is a joint work with Nicolae Vulpe.