dc.contributor.author
Fukui, T.
dc.contributor.author
Nuño Ballesteros, Juan José
dc.identifier
https://ddd.uab.cat/record/85167
dc.identifier
urn:10.5565/PUBLMAT_56112_03
dc.identifier
urn:oai:ddd.uab.cat:85167
dc.identifier
urn:articleid:20144350v56n1p65
dc.identifier
urn:oai:raco.cat:article/248359
dc.identifier
urn:scopus_id:84856925461
dc.identifier
urn:wos_id:000299578800003
dc.description.abstract
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.
dc.format
application/pdf
dc.relation
Publicacions matemàtiques ; Vol. 56, Num. 1 (2012), p. 65-89
dc.rights
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dc.rights
https://rightsstatements.org/vocab/InC/1.0/
dc.subject
Totally real differential form
dc.subject
Principal lines
dc.subject
Darbouxian umbilics
dc.title
Isolated singularities of binary differential equations of degree n
