A Fundamental Property of Monge Characteristics in Involutive Systems of Non-Linear Partial Differential Equations and its Application.
A general controllability theorem
Abnormal curves on the Goursat systems of .
Algèbres de Lie libres associées a un système de Pfaff.
By using an invariant related to free Lie algebras, we give a criterion of non existence of isomorphism for the Pfaffian systems.
An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms
We give a proof of the fact that any holomorphic Pfaffian form in two variables has a convergent integral curve. The proof gives an effective method to construct the solution, and we extend it to get a Gevrey type solution for a Gevrey form.
Applications de Dulac et applications pfaffiennes
Automorphisms of spatial curves.
Automorphisms of spatial curves
Automorphisms of curves , in are investigated; i.e. invertible transformations, where the coordinates of the transformed curve , depend on the derivatives of the original one up to some finite order . While in the two-dimensional space the problem is completely resolved (the only possible transformations are the well-known contact transformations), the three-dimensional case proves to be much more complicated. Therefore, results (in the form of some systems of partial differential equations...