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000085167 024 8_ $9 artpubuab $9 driver $a oai:ddd.uab.cat:85167
000085167 024 7_ $2 doi $a 10.5565/PUBLMAT_56112_03
000085167 035 __ $9 articleid $a 02141493v56n1p65
000085167 041 __ $a eng
000085167 100 __ $a Fukui, T.
000085167 245 1_ $a Isolated singularities of binary differential equations of degree n
000085167 520 3_ $a 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.
000085167 540 __ $9 info:eu-repo/semantics/restrictedAccess $a Tots els drets reservats $u http://www.europeana.eu/rights/rr-f/
000085167 546 __ $a Anglès.
000085167 599 __ $a recerca
000085167 653 1_ $a Totally real differential form
000085167 653 1_ $a Principal lines
000085167 653 1_ $a Darbouxian umbilics
000085167 653 1_ $a Index
000085167 655 _4 $a info:eu-repo/semantics/article
000085167 655 _4 $a info:eu-repo/semantics/publishedVersion
000085167 700 __ $a Nuño-Ballesteros, J. J.
000085167 773 __ $g Vol. 56, Núm. 1 ( 2012), p. 65-89 $t Publicacions matemàtiques $x 0214-1493
000085167 856 40 $p 25 $s 302304 $u http://ddd.uab.cat/uab/pubmat/02141493v56n1/pubmat_a2012v56n1p65.pdf
000085167 973 __ $f 0065 $l 89 $m  $n 1 $v 56 $x 02141493v56n1 $y 2012
000085167 980 __ $a ARTPUB $b PUBMAT $b UAB