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Regular and Chaotic Dynamics, 2018, Volume 23, Issue 7-8, Pages 842–849
DOI: https://doi.org/10.1134/S1560354718070031 (Mi rcd370) 		 
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
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DOI: https://doi.org/10.1134/S1560354718070031
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.
Funding agency Grant number
Russian Science Foundation 16-11-10069
The work was supported by the Russian Science Foundation (grant No. 16-11-10069).
Received: 16.10.2018
Accepted: 14.11.2018
Bibliographic databases:
Document Type: Article
MSC: 53C56, 35P20
Language: English
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
Citation in format AMSBIB
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\by Andrei I. Shafarevich
\paper The Maslov Complex Germ and Semiclassical Spectral Series Corresponding to Singular Invariant Curves of Partially Integrable Hamiltonian Systems
\jour Regul. Chaotic Dyn.
\yr 2018
\vol 23
\issue 7-8
\pages 842--849
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\crossref{https://doi.org/10.1134/S1560354718070031}
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