Geometry and Spectrum in 2D Magnetic Wells

Abstract

This paper is devoted to the classical mechanics and spectral analysis of a pure magnetic Hamiltonian in $\R^2$. 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.