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N. N. Nekhoroshev, D. A. Sadovskii, B. I. Zhilinskii (2002)
Fractional monodromy of resonant classical and quantum oscillatorsC. R. Acad. Sci. Paris, Ser. I, 335
R. Cushman, L. Bates (2004)
Global Aspects of Classical Integrable Systems
N. Nekhoroshev, D. Sadovskií, B. Zhilinskií (2002)
Fractional monodromy of resonant classical and quantum oscillatorsComptes Rendus Mathematique, 335
N. Mermin (1979)
The topological theory of defects in ordered mediaReviews of Modern Physics, 51
(1972)
Action-angle variables and their generalizationsTrans. Moscow Math. Soc., 26
B. I. Zhilinskií (2002)
Group 24: Physical and Mathematical Aspects of Symmetries
F. Faure, B. Zhilinskií (1999)
Topological chern indices in molecular spectraPhysical review letters, 85 5
M. Joyeux, D. Sadovskií, J. Tennyson (2003)
Monodromy of the LiNC/NCLi moleculeChemical Physics Letters, 382
F. Faure, B. Zhilinskií (2002)
Topologically coupled energy bands in moleculesPhysics Letters A, 302
L. Lerman, Ja. Umanskii (1994)
Four-Dimensional Integrable Hamiltonian Systems with Simple Singular Points
D. Carter, G. Keller (1983)
Bounded elementary generation of $\mathrm{SL}_{n}(\mathcal{O})$Amer. J. Math., 105
R. Cushman, B. Zhilinskií (2002)
Monodromy of a two degrees of freedom Liouville integrable system with many focus–focus singular pointsJournal of Physics A: Mathematical and General, 35
C. Soulé (2004)
An Introduction to Arithmetic GroupsarXiv: Group Theory
D. Sadovskií, B. Zhilinskií (1999)
Monodromy, diabolic points, and angular momentum couplingPhysics Letters A, 256
L. Lerman, Yan Umanskiy (1998)
Four-dimensional integrable Hamiltonian systems with simple singular points (topological aspects)
Richard Stanley (1986)
Enumerative Combinatorics
N. Zung (2001)
Another Note on Focus-Focus SingularitiesLetters in Mathematical Physics, 60
V. Matveev (1996)
Integrable Hamiltonian system with two degrees of freedom. The topological structure of saturated neighbourhoods of points of focus-focus and saddle-saddle typeSbornik Mathematics, 187
M. Child, T. Weston, J. Tennyson (1999)
Quantum monodromy in the spectrum of H2O and other systems: new insight into the level structure of quasi-linear moleculesMolecular Physics, 96
D. Sadovskií, B. Zhilinskií (1995)
Counting levels within vibrational polyads: Generating function approachJournal of Chemical Physics, 103
R. Cushman, H. Dullin, A. Giacobbe, Darryl Holm, M. Joyeux, P. Lynch, D. Sadovskií, B. Zhilinskií (2004)
CO2 molecule as a quantum realization of the 1:1:2 resonant swing-spring with monodromy.Physical review letters, 93 2
B. Zhilinskií (2003)
Hamiltonian monodromy as lattice defect, 150
L. Michel (2001)
Symmetry, invariants, topologyPhysics Reports, 341
A. Giacobbe, R. Cushman, D. Sadovskií, B. Zhilinskií (2004)
Monodromy of the quantum 1:1:2 resonant swing springJournal of Mathematical Physics, 45
K. Efstathiou, M. Joyeux, D. Sadovskií (2004)
Global bending quantum number and the absence of monodromy in the HCN-CNH moleculePhysical Review A, 69
L. Michel, B. Zhilinskií (2001)
Symmetry, invariants, topology. Basic toolsPhysics Reports, 341
R. Rankin (1977)
Modular Forms and Functions
J. Duistermaat (1980)
On global action‐angle coordinatesCommunications on Pure and Applied Mathematics, 33
R. Cushman, D. Sadovskií (2000)
Monodromy in the hydrogen atom in crossed fieldsPhysica D: Nonlinear Phenomena, 142
M. S. Child, T. Weston, J. Tennyson (1999)
Quantum monodromy in the spectrum of H2O and other systemsMol. Phys., 96
Y. Verdière, San Ngọc (2000)
SINGULAR BOHR-SOMMERFELD RULES FOR 2D INTEGRABLE SYSTEMSAnnales Scientifiques De L Ecole Normale Superieure, 36
D. Carter, G. Keller (1983)
BOUNDED ELEMENTARY GENERATION OF SL,n (0)American Journal of Mathematics, 105
L. Grondin, D. A. Sadovskií, B. I. Zhilinskií (2002)
Monodromy in systems with coupled angular momenta and rearrangement of bands in quantum spectraPhys. Rev. A, 65
H. Waalkens, A. Junge, H. Dullin (2003)
Quantum monodromy in the two-centre problemJournal of Physics A, 36
B. Zhilinskií (2001)
Symmetry, invariants, and topology in molecular modelsPhysics Reports, 341
L. Michel (1980)
SYMMETRY DEFECTS AND BROKEN SYMMETRY. CONFIGURATIONS - HIDDEN SYMMETRYReviews of Modern Physics, 52
N. Zung (1997)
A note on focus-focus singularitiesDifferential Geometry and Its Applications, 7
R. Cushman, Vu San (2002)
Sign of the Monodromy for Liouville Integrable SystemsAnnales Henri Poincaré, 3
L. Grondin, D. Sadovskií, B. Zhilinskií (2001)
Monodromy as topological obstruction to global action-angle variables in systems with coupled angular momenta and rearrangement of bands in quantum spectraPhysical Review A, 65
R. Cushman, J. Duistermaat (1988)
The quantum mechanical spherical pendulumBulletin of the American Mathematical Society, 19
The analogy between monodromy in dynamical (Hamiltonian) systems and defect in crystal lattices is used in order to formulate some general conjectures about possible types of qualitative features of quantum systems which can be interpreted as a manifestation of classical monodromy in quantum finite particle (molecular) problems.
Acta Applicandae Mathematicae – Springer Journals
Published: Jan 25, 2005
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