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Formes normales d'équations differéntielles implicites et de champs de Liouville

Published online by Cambridge University Press:  19 September 2008

M. Manouchehri
M. Manouchehri
Affiliation:
UFR de Mathématiques, CASE 7012, Université Denis Dierot, 2, Place Jussieu, 75251 Paris, Cédex 5, France
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Abstract

Consider the partial differential equation f(x, y(x), dy(x)) = 0, where f is a smooth real function on ℝn × ℝ × (ℝn)*. Near each singularity of the characteristic foliation, a Liouville field is associated to the equation; we classify hyperbolic germs of Liouville fields up to symplectic transformations, hence we deduce normal forms for partial differential equations up to transformations which preserve the standard contact form of ℝ2n+1. For n = 1, a theorem of Davydov enables us to deduce normal forms for such equations up to transformations of the x, y plane.

Type
Survey Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 4 , August 1996 , pp. 779 - 789
Copyright
Copyright © Cambridge University Press 1996

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References

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