2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76677The semi-classical study of a 1-dimensional Schrödinger operator near a non-degenerate maximum of the potential has lead Colin de Verdière and Parisse to prove a microlocal normal form theorem for any 1-dimensional pseudo-differential operator with the same kind of singularity. We present here a generalization of this result to pseudo-differential integrable systems of any finite degree of freedom with a Morse singularity. Our results are based upon Eliasson's study of critical integrable systems.1 figure, 28 pages, in french uses isolatin1.styAnalysis of PDEsDynamical Systems58F05, 57R70, 58G15, 58F36, 34C20, 81Q20, 81S05text