eng
Isolated singularities of binary differential equations of degree n
Fukui, T.
Nuño-Ballesteros, J. J.
info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
2012
Totally real differential form
Principal lines
Darbouxian umbilics
Index
Publicacions matemàtiques ; Vol. 56, Núm. 1 ( 2012), p. 65-89
http://ddd.uab.cat/record/85167
10.5565/PUBLMAT_56112_03
oai:ddd.uab.cat:85167
02141493v56n1p65
info:eu-repo/semantics/openAccess
Tots els drets reservats
http://www.europeana.eu/rights/rr-f/
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.
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