Isolated singularities of binary differential equations of degree "n"

• Autores: T. Fukui, J.J. Nuños Ballesteros
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 56, Nº 1, 2012, págs. 65-89
• Idioma: inglés
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• Resumen

  • We study isolated singularities of binary differential equations of degree n which are totally real. This means that at any regular point, the associated algebraic equation of degree n has exactly n different real roots (this generalizes the so called positive quadratic differential forms when n = 2). We introduce the concept of index for isolated singularities and generalize Poincar´e-Hopf theorem and Bendixson formula. Moreover, we give a classification of phase portraits of the n-web around a generic singular point. We show that there are only three types, which generalize the Darbouxian umbilics D1, D2 and D3.