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The Maslov Complex Germ and Semiclassical Spectral Series Corresponding to Singular Invariant Curves of Partially Integrable Hamiltonian Systems
Andrei I. Shafarevichabcd a National Research Centre “Kurchatov Institute”, pl. Akademika Kurchatova 1, Moscow, 123182 Russia
b Institute for Problems in Mechanics, pr. Vernadskogo 101-1, Moscow, 119526 Russia
c Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Vorob’evy gory, Moscow, 119899 Russia
d Moscow Institute of Physics and Technology, Inststitutskii per. 9, Dolgoprudnyi, Moscow, 141700 Russia
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.
Keywords:
semiclassical eigenvalues, complex vector bundles, holonomy group.
Received: 16.10.2018 Accepted: 14.11.2018
Citation:
Andrei I. Shafarevich, “The Maslov Complex Germ and Semiclassical Spectral Series Corresponding to Singular Invariant Curves of Partially Integrable Hamiltonian Systems”, Regul. Chaotic Dyn., 23:7-8 (2018), 842–849
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https://www.mathnet.ru/eng/rcd370 https://www.mathnet.ru/eng/rcd/v23/i7/p842
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Abstract page: | 183 | References: | 43 |
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