The semi-classical spectrum and the Birkhoff normal form
Mathematical Physics
2009-02-17 v1 math.MP
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.0902.2470,
title = {The semi-classical spectrum and the Birkhoff normal form},
author = {Yves Colin De Verdière},
journal= {arXiv preprint arXiv:0902.2470},
year = {2009}
}