Isotropic tori, complex germ and Maslov index, normal forms and quasimodes of multidimensional spectral problems (Q5951079)

More than twenty years ago V. P. Maslov proposed the following problem: Give sufficient conditions such that there exists a correspondence between isotropic lower-dimensional tori of Hamiltonian systems on one hand and the spectral series of the wave operators of the corresponding quantum system on the other hand. In the paper under review the authors give an answer to this problem in terms of the quadratic approximation and the theory of normal forms.