In a previous paper  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.
|Journal||Discrete and Continuous Dynamical Systems - Series A (DCDS-A)|
|Publication status||Published - 1997|
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