85167 artpubuab driver oai:ddd.uab.cat:85167 articleid 02141493v56n1p65 doi 10.5565/PUBLMAT_56112_03 eng Fukui, T. Isolated singularities of binary differential equations of degree n 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 http://www.europeana.eu/rights/rr-f/ Article de fons Totally real differential form Principal lines Darbouxian umbilics Index info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Nuño-Ballesteros, J. J. Vol. 56, Núm. 1 ( 2012), p. 65-89 Publicacions matemàtiques 0214-1493 25 302304 http://ddd.uab.cat/uab/pubmat/02141493v56n1/pubmat_a2012v56n1p65.pdf 0065 89 1 56 02141493v56n1 2012 ARTPUB PUBMAT UAB file 0 MD5 dfb14a3411154c1a39bfb2227a4a9b5c 302304 bytestream 1.6 filepath uab/pubmat/02141493v56n1/pubmat_a2012v56n1p65.pdf disk