Real isolated singularity. (Q1175680)

The author takes a germ of analytic functions \(f: (\mathbb{R}^{n+1},0)\to(\mathbb{R},0)\) \((n\geqq 1)\), with isolated singularity at \(0\in\mathbb{R}^{n+1}\). He proposes to study the asymptotic expansion of integrals obtained by integration of \(C_ 0^{\infty}\) forms, with degree \(n\), over the fiber of \(f\). He describes these asymptotic expansions by the monodromy action on the group \(H^ n\) of the complex Milner fiber. He also gives several interesting examples.