Abstract:

In this talk we consider the reversible cubic vector fields of the form [x' = −y + ax^2 + bxy + cy^2 − y(x^2 + y^2),] [y' = x + dx^2 + exy + fy^2 + x(x^2 + y^2),] having simultaneously a center at infinity and at the origin. Attention goes to a subclass of these reversible systems having collinear or infinitely many singularities and the systematic classification of their global phase portraits with respect to topological and diffeomorphic equivalence.

This is a joint work with Jaume Llibre and Joan Torregrosa.