The semi-classical spectrum and the Birkhoff normal form

Details The semi-classical spectrum and the Birkhoff normal form The semi-classical spectrum and the Birkhoff normal form

2009-02-14

arxiv.org/abs/0902.2470v1

Physics

Mathematical Physics

Scientific paper

The purposes of this note are: 1) to propose a direct and "elementary" proof of the main result proved by Guillemin-Paul-Uribe [GPU], namely that the semi-classical spectrum near a global minimum of the classical Hamiltonian determines the whole semi-classical Birkhoff normal form (denoted the BNF) in the non-resonant case. 2) to present in the completely resonant case a similar problem.

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