eng Isolated singularities of binary differential equations of degree n Fukui, T. Nuño-Ballesteros, J. J. info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 2012 Totally real differential form Principal lines Darbouxian umbilics Index Publicacions matemàtiques http://ddd.uab.cat/record/85167 oai:ddd.uab.cat:85167 02141493v56n1p65 10.5565/PUBLMAT_56112_03 Tots els drets reservats http://www.europeana.eu/rights/rr-f/ 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.