Bifurcations of implicit differential equations

J.W. Bruce, G. Fletcher, F. Tari

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

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)
Original languageEnglish
Pages (from-to)485-506
JournalProceedings of the Royal Society of Edinburgh: Section A Mathematics
Volume130
Issue number3
Publication statusPublished - 2000

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Implicit Differential Equations
Bifurcation
Smooth surface
Discriminant
Smooth function
Singularity
Binary
Curve
Model
Family

Cite this

Bruce, J.W. ; Fletcher, G. ; Tari, F. / Bifurcations of implicit differential equations. In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 2000 ; Vol. 130, No. 3. pp. 485-506.
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Bifurcations of implicit differential equations. / Bruce, J.W.; Fletcher, G.; Tari, F.

In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 130, No. 3, 2000, p. 485-506.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Bifurcations of implicit differential equations

AU - Bruce, J.W.

AU - Fletcher, G.

AU - Tari, F.

PY - 2000

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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

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ER -