Spectrum of semiclassical Schrödinger operators for two-frequency resonance

Abstract

This article is devoted to an analysis of semiclassical Schrödinger operators for two-frequency resonance of the type 1 : p where p is even. The Birkhoff–Gustavson normal form is applied to describe the discrete spectrum in the case where the potential is smooth and admits a nondegenerate global minimum at the origin 0.