Bifurcations of implicit differential equations

Bruce, J.W., Fletcher, G. and Tari, F. (2000) Bifurcations of implicit differential equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 130 (3). pp. 485-506. ISSN 0308-2105

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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)

Item Type: Article
Subjects: Q Science > QA Mathematics
Date Deposited: 04 Dec 2010 12:31
URI: http://repository.edgehill.ac.uk/id/eprint/1527

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