Index of an implicit differential equation

In this paper we introduce the concept of the index of an implicit differential equation F(x, y, p) = 0, where F is a smooth function, $P = \frac{{dy}}{{dx}}$, Fp= 0 and Fpp = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in ℝ⁵.

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Veröffentlicht in:	Publicacions matemàtiques 2010-01, Vol.54 (1), p.173-186
Hauptverfasser:	Challapa, L. S, Ruas, M. A. S
Format:	Artikel
Sprache:	eng
Schlagworte:	34A09 34A26 58K05 binary differential equation Coefficients Curves Differential equations Discriminants Geometric planes Index Mathematical cusps Mathematical surfaces quadratic differential form Smooth surfaces Vector fields
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Beschreibung
Zusammenfassung:	In this paper we introduce the concept of the index of an implicit differential equation F(x, y, p) = 0, where F is a smooth function, $P = \frac{{dy}}{{dx}}$, Fp= 0 and Fpp = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in ℝ⁵.
ISSN:	2014-4350 0214-1493 2014-4350
DOI:	10.5565/PUBLMAT_54110_10