On the Geometry in the Neighborhood of Quadratic Differential System with a Weak Focus

• Autores: Janos Pal, Dana Schlomiuk
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 2, Nº 1, 2001, págs. 1-44
• Idioma: inglés
• DOI: 10.1007/bf02969379
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• Resumen

  • In this work we use the algebro-geometric concept of divisor on a projective curve in the study of planar quadratic vector fields. We introduce here specific divisors to encode global information about the geometry at infinity of quadratic systems with a weak focus which is not a center and we show that these concepts organise and unify in an intrinsic way this information. This geometric approach forms a link between chart-dependent classification studies of quadratic (or cubic) differential systems and affine-invariant results based on the algebraic theory of invariants of differential systems.