A set on which the local Łojasiewicz exponent is attained
Let U be a neighbourhood of 0 ∈ ℂⁿ. We show that for a holomorphic mapping , F(0) = 0, the Łojasiewicz exponent ₀(F) is attained on the set z ∈ U: f₁(z)·...·fₘ(z) = 0.
La forme hermitienne canonique sur la partie invariante de la cohomologie de la fibre de Milnor d'une singularité isolée de polynôme quasi-homogène
Linking numbers and boundaries of varieties.
Microlocal analysis of diffraction by a corner
Multiplicity of polynomials on trajectories of polynomial vector fields in
Let ξ be a polynomial vector field on with coefficients of degree d and P be a polynomial of degree p. We are interested in bounding the multiplicity of a zero of a restriction of P to a non-singular trajectory of ξ, when P does not vanish identically on this trajectory. Bounds doubly exponential in terms of n are already known ([9,5,10]). In this paper, we prove that, when n=3, there is a bound of the form . In Control Theory, such a bound can be used to give an estimate of the degree of nonholonomy...
On splitting up singularities of fundamental solutions to elliptic equations in ℂ2
It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in ℂ2. In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.
Premiers pas en calcul étranger
Cet exposé est une introduction au calcul étranger d’Écalle, c’est-à-dire au calcul des obstructions à la sommabilité de Borel d’une grande classe de séries formelles, les fonctions résurgentes d’Écalle. La théorie d’Écalle éclaire d’un jour neuf le célèbre phénomène de Stokes qui est illustré ici dans le contexte de la méthode du col.