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Isolated singularities of binary differential equations of degree n Fukui, T. Nuño Ballesteros, Juan José Totally real differential form Principal lines Darbouxian umbilics Index 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. 2012 Article https://ddd.uab.cat/record/85167 urn:10.5565/PUBLMAT_56112_03 urn:oai:ddd.uab.cat:85167 urn:articleid:20144350v56n1p65 urn:oai:raco.cat:article/248359 urn:scopus_id:84856925461 urn:wos_id:000299578800003 eng Publicacions matemàtiques ; Vol. 56, Num. 1 (2012), p. 65-89 open access Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets. https://rightsstatements.org/vocab/InC/1.0/ application/pdf