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

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  • In a previous paper [2] we made a classification of generic binary differential equations (BDE's)


    near points at which the discriminant function $b^2-ac$ 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 $2\times 2$ matrices. It also sheds light on the structure of the rarefraction curves associated to a $2\times 2$ system of conservation laws in 1 space variable.

    Mathematics Subject Classification: 58Fxx, 34Cxx.


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