Generic 1-parameter families of binary differential equations of Morse type

J.W. Bruce, F. Tari

    Research output: Contribution to journalArticle

    19 Citations (Scopus)

    Abstract

    In a previous paper [2] we made a classification of generic binary differential equations (BDE's) near points at which the discriminant function has a Morse singularity. Such points occur naturally in families of BDE's and here we describe the manner in which the configuration of solution curves change in their natural 1-parameter versal deformations. The results in this paper can be used to describe, for instance, the changes in the structure of the asymptotic curves on a 1-parameter family of smooth surfaces acquiring a flat umbilic and on integral curves determined by eigenvectors of 1-parameter families of matrices. It also sheds light on the structure of the rarefraction curves associated to a system of conservation laws in 1 space variable. Mathematics Subject Classification: 58Fxx, 34Cxx.
    Original languageEnglish
    Pages (from-to)79-90
    JournalDiscrete and Continuous Dynamical Systems - Series A (DCDS-A)
    Volume3
    Issue number1
    DOIs
    Publication statusPublished - 1997

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