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.
Keywords:
semiclassical eigenvalues, complex vector bundles, holonomy group
Citation:
Shafarevich A. I., The Maslov Complex Germ and Semiclassical Spectral Series Corresponding to Singular Invariant Curves of Partially Integrable Hamiltonian Systems, Regular and Chaotic Dynamics,
2018, Volume 23, Numbers 7-8,
pp. 842-849