Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-02T12:29:34.157Z Has data issue: false hasContentIssue false
  • English
  • Français

Bifurcations of implicit differential equations

Published online by Cambridge University Press:  11 July 2007

J. W. Bruce ,
G. J. Fletcher  and
F. Tari
J. W. Bruce
Affiliation:
Department of Pure Mathematics, The University of Liverpool, PO Box 147, Liverpool L69 3BX, UK ([email protected])
G. J. Fletcher
Affiliation:
Department of Pure Mathematics, The University of Liverpool, PO Box 147, Liverpool L69 3BX, UK ([email protected])
F. Tari
Affiliation:
Instituto de Ciências, Matemáticas e de Computação, Universidade de São Paulo, Caixa Postal 668, CEP 13560-970, São Carlos (SP), Brasil ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we give a local classification of the integral curves of implicit differential equations where F is a smooth function and p = dy/dx, at points where Fp = 0, Fpp ≠ 0 and where the discriminant {(x, y) : F = Fp = 0} has a Morse singularity. We also produce models for generic bifurcations of such equations and apply the results to the differential geometry of smooth surfaces. This completes the local classification of generic one-parameter families of binary differential equations (BDEs).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 130 , Issue 3 , June 2000 , pp. 485 - 506
Copyright
Copyright © Royal Society of Edinburgh 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)