The Maslov Complex Germ and Semiclassical Spectral Series Corresponding to Singular Invariant Curves of Partially Integrable Hamiltonian Systems

Abstract

We study semiclassical eigenvalues of the Schroedinger operator, corresponding to singular invariant curve of the corresponding classical system. The latter system is assumed to be partially integrable. We describe geometric object corresponding to the eigenvalues (comlex vector bundle over a graph) and compute semiclassical eigenvalues in terms of the corresponding holonomy group.