On binary differential equations
- 1 March 1995
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 8 (2) , 255-271
- https://doi.org/10.1088/0951-7715/8/2/008
Abstract
In this paper we give the local classification of solution curves of binary differential equations a(x,y)dy2+2b(x,y)dxdy+c(x,y)dx2=0 at points at which the discriminant function b2-ac has a Morse singularity. We also discuss the formal reduction of such equations to some normal form. The results determine the topological structure of asymptotic curves on a smooth surface with a flat umbilic, the principal curves at general umbilics, and asymptotic curves at cross-cap points of an otherwise smooth surface.Keywords
This publication has 2 references indexed in Scilit:
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- Normal form of a differential equation, not solvable for the derivative, in a neighborhood of a singular pointFunctional Analysis and Its Applications, 1985