The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
The authors of this paper intend to show that one can obtain certain spectral series if the Hamiltonian system possesses only one (individual) invariant Lagrangian torus with almost periodic or periodic motion and explain how one can obtain such tori using the Maupertuis-Jacobi correspondence. In this respect, the authors have shown that the existence of almost invariant Lagrangian tori follows from the Darboux-Weinstein theorem for general Lagrangian manifolds, and they give a simpler proof and sufficiently explicit formulas in the case considered. The present theory is applied to water wave theory by observing that a Hamiltonian operator \(\chi (x,p ) = g(x) p^2\) is determined by a Liouville metric \(g (x)\) in a plane domain \(\Omega\) diffeomorphic to an annulus.
scientific article; zbMATH DE number 5791067