On binary differential equations

J.W. Bruce, F. Tari

    Research output: Contribution to journalArticle

    39 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)255-271
    JournalNonlinearity
    Volume8
    Issue number2
    DOIs
    Publication statusPublished - 1995

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