Tracing phase portraits of planar polynomial vector fields with detailed analysis of the singularities

The paper essentially aims at presenting a computer program drawing phase portraits of planar polynomial vector fields. It is essentially based on a detailed analysis of the singularities by means of desingularization using quasihomogeneous blow-up and the Newton diagram, and good approximation of invariant manifolds. Phase portraits can be drawn locally near a singularity or globally on a Poincaré disc or a Poincaré-Lyapunov disc, compactifying the plane. © 1999 Birkhäuser-Verlag.