Sur le spectre semi-classique d'un syst\`eme int\'egrable de dimension 1 autour d'une singularit\'e hyperbolique

Abstract

In this article we describe the semi-classical spectrum of a Schrodinger operator on $\mathbb{R}$ with a double well potential. We study the shape of spectrum around the local maximum of the potential. In the classification of singularities of integrable systems, the double wells is the model of non-degenerate hyperbolic singularity.