### 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 language | English |
---|---|

Pages (from-to) | 79-90 |

Journal | Discrete and Continuous Dynamical Systems - Series A (DCDS-A) |

Volume | 3 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1997 |

## Fingerprint Dive into the research topics of 'Generic 1-parameter families of binary differential equations of Morse type'. Together they form a unique fingerprint.

## Cite this

Bruce, J. W., & Tari, F. (1997). Generic 1-parameter families of binary differential equations of Morse type.

*Discrete and Continuous Dynamical Systems - Series A (DCDS-A)*,*3*(1), 79-90. https://doi.org/10.3934/dcds.1997.3.79