### Abstract

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

### Cite this

*Discrete and Continuous Dynamical Systems - Series A (DCDS-A)*,

*3*(1), 79-90. https://doi.org/10.3934/dcds.1997.3.79

}

*Discrete and Continuous Dynamical Systems - Series A (DCDS-A)*, vol. 3, no. 1, pp. 79-90. https://doi.org/10.3934/dcds.1997.3.79

**Generic 1-parameter families of binary differential equations of Morse type.** / Bruce, J.W.; Tari, F.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Generic 1-parameter families of binary differential equations of Morse type

AU - Bruce, J.W.

AU - Tari, F.

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

U2 - 10.3934/dcds.1997.3.79

DO - 10.3934/dcds.1997.3.79

M3 - Article

VL - 3

SP - 79

EP - 90

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 1

ER -