Bifurcations of implicit differential equations

J.W. Bruce, G. Fletcher, F. Tari

    Research output: Contribution to journalArticle

    24 Citations (Scopus)

    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 languageEnglish
    Pages (from-to)485-506
    JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
    Volume130
    Issue number3
    Publication statusPublished - 2000

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