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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 Poincaré-Hopf theorem and Bendixson formula. Moreover, we give a classification of phase portraits of the n-web around adoi:10.5565/publmat_56112_03 fatcat:ltfuu5og25honbbimfqnftl7gu