Cet article est consacré à la mécanique classique et l’analyse spectrale d’un hamiltonien purement magnétique dans . On démontre que la dynamique et la théorie spectrale semi-classique peuvent être traitées par une forme normale de Birkhoff, et ainsi réduites à l’étude d’une famille d’hamiltoniens à un degré de liberté. Corollairement, on obtient une extension de résultats récents de Helffer et Kordyukov à de plus hautes énergies.
This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in . It is established that both the dynamics and the semiclassical spectral theory can be treated through a Birkhoff normal form and reduced to the study of a family of one dimensional Hamiltonians. As a corollary, recent results by Helffer-Kordyukov are extended to higher energies.
@article{AIF_2015__65_1_137_0,
author = {Raymond, Nicolas and V\~u Ng\d oc, San},
title = {Geometry and Spectrum in 2D Magnetic Wells},
journal = {Annales de l'Institut Fourier},
volume = {65},
year = {2015},
pages = {137-169},
doi = {10.5802/aif.2927},
zbl = {1327.81207},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2015__65_1_137_0}
}
Raymond, Nicolas; Vũ Ngọc, San. Geometry and Spectrum in 2D Magnetic Wells. Annales de l'Institut Fourier, Tome 65 (2015) pp. 137-169. doi : 10.5802/aif.2927. http://gdmltest.u-ga.fr/item/AIF_2015__65_1_137_0/
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