### Abstract

Original language | English |
---|---|

Pages (from-to) | 485-506 |

Journal | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |

Volume | 130 |

Issue number | 3 |

Publication status | Published - 2000 |

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### Cite this

*Proceedings of the Royal Society of Edinburgh: Section A Mathematics*,

*130*(3), 485-506.

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*Proceedings of the Royal Society of Edinburgh: Section A Mathematics*, vol. 130, no. 3, pp. 485-506.

**Bifurcations of implicit differential equations.** / Bruce, J.W.; Fletcher, G.; Tari, F.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Bifurcations of implicit differential equations

AU - Bruce, J.W.

AU - Fletcher, G.

AU - Tari, F.

PY - 2000

Y1 - 2000

N2 - In this paper we give a local classi¯cation of the integral curves of implicit di®erential equations F (x; y; p) = 0; where F is a smooth function and p = dy=dx, at points where Fp = 0, Fpp =6 0 and where the discriminant f(x; y) : F = Fp = 0g has a Morse singularity. We also produce models for generic bifurcations of such equations and apply the results to the di®erential geometry of smooth surfaces. This completes the local classi¯cation of generic one-parameter families of binary di®erential equations (BDEs)

AB - In this paper we give a local classi¯cation of the integral curves of implicit di®erential equations F (x; y; p) = 0; where F is a smooth function and p = dy=dx, at points where Fp = 0, Fpp =6 0 and where the discriminant f(x; y) : F = Fp = 0g has a Morse singularity. We also produce models for generic bifurcations of such equations and apply the results to the di®erential geometry of smooth surfaces. This completes the local classi¯cation of generic one-parameter families of binary di®erential equations (BDEs)

M3 - Article

VL - 130

SP - 485

EP - 506

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 3

ER -