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

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