- 01-164 Colin de Verdi re, Yves
- SINGULAR LAGRANGIAN MANIFOLDS AND SEMI-CLASSICAL ANALYSIS
May 2, 01
(auto. generated ps),
of related papers
Abstract. Lagrangian submanifolds of symplectic manifolds are very central
objects in classical mechanics and microlocal analysis.
These manifolds are frequently singular
(integrable systems, bifurcations, reduction). There has been a
lot of works on singular Lagrangian manifolds initiated
by Arnold, Givental and others.
The goal of our paper is to extend the classical and semi-classical
normal forms of completely integrable systems near non degenerate
singularities to more singular systems.
It turns out that there is a nicely working way to do that, leading
to normal forms and universal unfoldings. We obtain this way natural
Ansatz's extending the WKB-Maslov Ansatz.
We give more details on the
simplest non Morse example, the cusp, which corresponds to a