Symplectic Techniques for Semiclassical Completely Integrable Systems

2004/07/28 by San Vu Ngoc, Ngoc, San Vu
Mathematics · #34C20 #37J35 #53D #58J40 #58K45 #70H06 #81Q10 #81S10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP) #Symplectic Geometry (math.SG) #math.AP #math.SG #math.SP #msc:34C20 #msc:37J35 #msc:53D #msc:58J40 #msc:58K45 #msc:70H06 #msc:81Q10 #msc:81S10

paper · pdf · doi:10.48550/arxiv.math/0407477

32 pages, 7 figures. Review article

arxiv created 2004/07/28 · arxiv updated 2009/12/01

Abstract

This article is a survey of classical and quantum completely integrable systems from the viewpoint of local ``phase space'' analysis. It advocates the use of normal forms and shows how to get global information from glueing local pieces. Many crucial phenomena such as monodromy or eigenvalue concentration are shown to arise from the presence of non-degenerate critical points.

Related

• A PDE-Based Approach to Classical Phase-Space Deformations
• Symplectic Topology of Integrable Hamiltonian Systems, II: Topological Classification
• Symplectic invariants of semitoric systems and the inverse problem for quantum systems
• Lectures on integrable Hamiltonian systems
• Symplectic approach to global stability