Singularites reelles isolees et developpements asymptotiques d'integrales oscillantes

الأصل · EN

Let (Xᵣ, 0) be a germ of real analytic subset in (Rⁿ, 0) of pure dimension n+1 with an isolated singularity at 0. Let (fᵣ,0): (Xᵣ, 0) --> (R,0) a real analytic germ with an isolated singularity at 0, such that its complexification fC vanishes on the singular set S of XC. We also assume that Xᵣ-[0] is orientable. To each A ∈ H⁰(Xᵣ - 0,C) we associate a n-cycle Γ(A) ("explicitly " described) in the complex Milnor fiber of fC at 0 such that the non trivial terms in the asymptotic expansions of the oscillating integrals ∫ₐ eⁱτᶠ⁽ˣ⁾ ϕ(x) when τ→ ± ∞ can be read from the spectral decomposition of Γ(A) relative to the monodromy of fC at 0.