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

• Autores: Chris Herssens, Freddy Dumortier
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 1, Nº 1, 1999, págs. 97-131
• Idioma: inglés
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• Resumen

  • 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 Poincaré disc or a Poincaré-Lyapunov disc, compactifying the plane.