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Formes normales semi-classiques des systemes completement integrables au voisinage d'un point critique de l'application moment

Vu Ngoc San
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Abstract

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.

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Vu Ngoc San. 1998-03-09. Formes normales semi-classiques des systemes completement integrables au voisinage d'un point critique de l'application moment. https://arxiv.org/abs/math/9803027

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