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No monodromy in the champagne bottle, or singularities of a superintegrable system
1. | Department of Mathematics, University of Calgary, Calgary, AB, T2N 1N4 |
2. | Università di Padova, Dipartimento di Matematica Pura e Applicata, Via Trieste 63, 35121 Padova |
References:
[1] |
V. I. Arnol'd, Mathematical Methods of Classical Mechanics,, $2^{nd}$ edition, 60 (1989).
doi: 10.1007/978-1-4757-2063-1. |
[2] |
L. Bates, Monodromy in the champagne bottle,, Journal of Applied Mathematics and Physics (ZAMP), 42 (1991), 837.
doi: 10.1007/BF00944566. |
[3] |
R. Cushman and L. Bates, Global Aspects of Classical Integrable Systems,, $2^{nd}$ edition, (2015).
doi: 10.1007/978-3-0348-0918-4. |
[4] |
P. Dazord and T. Delzant, Le probleme general des variables actions-angles,, Journal of Differential Geometry, 26 (1987), 223.
|
[5] |
J. Duistermaat, On global action-angle coordinates,, Communications on Pure and Applied Mathematics, 33 (1980), 687.
doi: 10.1002/cpa.3160330602. |
[6] |
H. Dullin and H. Hanßmann, The degenerate C. Neumann system I: symmetry reduction and convexity,, Central European Journal of Mathematics, 10 (2012), 1627.
doi: 10.2478/s11533-012-0085-8. |
[7] |
F. Fassò, Superintegrable Hamiltonian systems: Geometry and perturbations,, Acta Applicandae Mathematicae, 87 (2005), 93.
doi: 10.1007/s10440-005-1139-8. |
[8] |
J. Milnor and J. Stasheff, Characteristic Classes,, Annals of mathematics studies 76, 76 (1974).
|
[9] |
A. Mischenko and A. Fomenko, Generalized Liouville method of integration of Hamiltonian systems,, Funct. Anal. Appl, 12 (1978), 113. Google Scholar |
[10] |
N. N. Nekhoroshev, Action-angle variables and their generalizations,, Trans. Moskow Math. Soc., 26 (1972), 181.
|
[11] |
M. Winnewisser, B. P. Winnewisser, F. C. De Lucia, I. R. Medvedev, S. C. Ross and L. M. Bates, The hidden kernel of molecular quasi-linearity: Quantum monodromy,, Journal of Molecular Structure, 798 (2006), 1.
doi: 10.1016/j.molstruc.2006.06.036. |
show all references
References:
[1] |
V. I. Arnol'd, Mathematical Methods of Classical Mechanics,, $2^{nd}$ edition, 60 (1989).
doi: 10.1007/978-1-4757-2063-1. |
[2] |
L. Bates, Monodromy in the champagne bottle,, Journal of Applied Mathematics and Physics (ZAMP), 42 (1991), 837.
doi: 10.1007/BF00944566. |
[3] |
R. Cushman and L. Bates, Global Aspects of Classical Integrable Systems,, $2^{nd}$ edition, (2015).
doi: 10.1007/978-3-0348-0918-4. |
[4] |
P. Dazord and T. Delzant, Le probleme general des variables actions-angles,, Journal of Differential Geometry, 26 (1987), 223.
|
[5] |
J. Duistermaat, On global action-angle coordinates,, Communications on Pure and Applied Mathematics, 33 (1980), 687.
doi: 10.1002/cpa.3160330602. |
[6] |
H. Dullin and H. Hanßmann, The degenerate C. Neumann system I: symmetry reduction and convexity,, Central European Journal of Mathematics, 10 (2012), 1627.
doi: 10.2478/s11533-012-0085-8. |
[7] |
F. Fassò, Superintegrable Hamiltonian systems: Geometry and perturbations,, Acta Applicandae Mathematicae, 87 (2005), 93.
doi: 10.1007/s10440-005-1139-8. |
[8] |
J. Milnor and J. Stasheff, Characteristic Classes,, Annals of mathematics studies 76, 76 (1974).
|
[9] |
A. Mischenko and A. Fomenko, Generalized Liouville method of integration of Hamiltonian systems,, Funct. Anal. Appl, 12 (1978), 113. Google Scholar |
[10] |
N. N. Nekhoroshev, Action-angle variables and their generalizations,, Trans. Moskow Math. Soc., 26 (1972), 181.
|
[11] |
M. Winnewisser, B. P. Winnewisser, F. C. De Lucia, I. R. Medvedev, S. C. Ross and L. M. Bates, The hidden kernel of molecular quasi-linearity: Quantum monodromy,, Journal of Molecular Structure, 798 (2006), 1.
doi: 10.1016/j.molstruc.2006.06.036. |
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