  We extend to the semi-classical setting the Maupertuis-Jacobi correspondance
for a pair of hamiltonians $(H(x,hD_x), {\cal H}(x,hD_x)$. If ${\cal H}(p,x)$
is completely integrable, or has merely has invariant diohantine torus
$\Lambda$ in energy surface ${\cal E}$, then we can construct a family of
quasi-modes for $H(x,hD_x)$ at the corresponding energy $E$. This applies in
particular to the theory of water-waves in shallow water, and determines
trapped modes by an island, from the knowledge of Liouville metrics.
