1998/03/09 by Vu Ngoc San, Vũ Ngoc San, San, Vu Ngoc
Mathematics · Physics and Astronomy · #34C20 #57R70 #58F05 #58F36 #58G15 #81Q20 #81S05 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.AP #math.DS #msc:34C20 #msc:57R70 #msc:58F05 #msc:58F36 #msc:58G15 #msc:81Q20 #msc:81S05
paper · pdf · doi:10.48550/arxiv.math/9803027
1 figure, 28 pages, in french uses isolatin1.sty
arxiv created 1998/03/09 · openalex publication_date 1998/03/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The 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.