Bifurcations of ordinary differential equations of Clairaut type

DOI10.1016/S0022-0396(02)00198-5zbMath1021.37031OpenAlexW2054583842MaRDI QIDQ1811803

Masatomo Takahashi

Publication date: 17 June 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-0396(02)00198-5

zbMATH Keywords

bifurcationnormal formssingularity theoryordinary differential equations of Clairaut type

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Normal forms on manifolds (58K50) Ordinary differential equations and systems on manifolds (34C40)

Related Items (6)

On implicit second-order ordinary differential equations: Completely integrable and Clairaut type ⋮ On approximate solutions of a class of Clairaut's equations ⋮ Bifurcations of completely integrable 2-variable first-order partial differential equations ⋮ ON IMPLICIT SECOND-ORDER PDE OF A SCALAR FUNCTION ON A PLANE VIA DIFFERENTIAL SYSTEMS ⋮ Bifurcations of completely integrable first-order ordinary differential equations ⋮ On families of Lagrangian submanifolds

Cites Work

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• Reconstructions of fronts and caustics depending on a parameter and versality of mappings
• Holonomic systems of Clairaut type
• The unfolding and determinacy theorems for subgroups of 𝒜 and 𝒦
• Isotopies of generic plane curves
• LOCAL CLASSIFICATION OF NON-LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
• The theory of Legendrian unfoldings and first-order differential equations
• CLASSIFICATION OF GENERIC INTEGRAL DIAGRAMS AND FIRST ORDER ORDINARY DIFFERENTIAL EQUATIONS
• Completely integrable holonomic systems of first-order differential equations

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