Abstract
In this paper we give a local classi¯cation of the integral curves of implicit di®erential
equations
F (x; y; p) = 0;
where F is a smooth function and p = dy=dx, at points where Fp = 0, Fpp =6 0 and
where the discriminant f(x; y) : F = Fp = 0g has a Morse singularity. We also
produce models for generic bifurcations of such equations and apply the results to the
di®erential geometry of smooth surfaces. This completes the local classi¯cation of
generic one-parameter families of binary di®erential equations (BDEs)
Original language | English |
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Pages (from-to) | 485-506 |
Journal | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
Volume | 130 |
Issue number | 3 |
Publication status | Published - 2000 |