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References (13)
-
S.Yu. Dobrokhotov, A. I. Shafarevich (1998)
Topological Methods in the Theory of Hamiltonian Systems -
(1992)
Semiclassical Maslov Asymptotics with Complex Phases: 1 -
A. Bolsinov, A. Fomenko (2004)
Integrable Hamiltonian Systems: Geometry, Topology, Classification -
V.P. Maslov (1976)
Operational Methods -
V. Maslov (1994)
The complex WKB method for nonlinear equations I -
(1998)
Semiclassical Quantization of Invariant Isotropic Manifolds, in Topological Methods in the Theory of Hamiltonian Systems, A.V.Bolsinov -
V.V. Belov, S.Yu. Dobrokhotov (1992)
SemiclassicalMaslov Asymptotics with Complex Phases: 1. General ApproachTheoret. and Math. Phys., 92
-
E. Harrell (1996)
The Complex WKB Method for Nonlinear Equations 1: Linear Theory (Victor P. Maslov)SIAM Rev., 38
-
(1976)
Operational Methods, Moscow: Mir -
J. Ralston (1979)
On the construction of quasimodes associated with stable periodic orbitsCommunications in Mathematical Physics, 67
-
V. Babich (1970)
Eigenfunctions Concentrated in a Neighborhood of a Closed Geodesic -
J. Duistermaat, V. Guillemin (1975)
The spectrum of positive elliptic operators and periodic bicharacteristicsInventiones mathematicae, 29
-
Yves Verdière, Bernard Parisse (1999)
Singular Bohr–Sommerfeld RulesCommunications in Mathematical Physics, 205
- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Dynamical Systems and Ergodic Theory
- ISSN
- 1560-3547
- eISSN
- 1468-4845
- DOI
- 10.1134/S1560354718070031
- Publisher site
- See Article on Publisher Site
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.
Journal
Regular and Chaotic Dynamics – Springer Journals
Published: Feb 7, 2019