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Isolated singularities of binary differential equations of degree n
Fukui, T.
Nuño-Ballesteros, J. J.

Data: 2012
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: Totally real differential form ; Principal lines ; Darbouxian umbilics ; Index
Publicat a: Publicacions matemàtiques, Vol. 56, Núm. 1 ( 2012) , p. 65-89, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_56112_03


25 p, 295.2 KB

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