||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.
||Tots els drets reservats
||article ; publishedVersion
Totally real differential form ;
Principal lines ;
Darbouxian umbilics ;
||Publicacions matemàtiques, Vol. 56, Núm. 1 ( 2012) , p. 65-89, ISSN 0214-1493