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Regular and Chaotic Dynamics

, Volume 23, Issue 7–8, pp 842–849 | Cite as

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

  • Andrei I. ShafarevichEmail author
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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 

MSC2010 numbers

53C56 35P20 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and MathematicsLomonosov Moscow State UniversityVorob’evy gory, MoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyMoscowRussia
  3. 3.Institute for Problems in MechanicsMoscowRussia
  4. 4.National Research Centre “Kurchatov Institute”MoscowRussia

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