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

Abstract

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 quasi-homogeneous 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 Poincare disc or a Poincare-Lyapunov disc, compactifying the plane.