Monodromy in the hydrogen atom in crossed fields

Physica D: Nonlinear Phenomena

Volumn 142, Issue 1-2, 2000, Pages 166-196

  Cushman, R H ^a   Sadovskii D A ^b  

^a UTRECHT UNIVERSITY   (Netherlands)

^b UNIVERSITÉ DU LITTORAL CÔTE D OPALE   (France)

Author keywords

Energy momentum map; Monodromy; Singular reduction

Indexed keywords

EID: 0347450519     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00053-1     Document Type: Article

References (65)

1. J.J. Duistermaat, Comm. Pure Appl. Math. 33 (1980) 687.
2. R.H. Cushman, L.M. Bates, Global Aspects of Classical Integrable Systems, Birkhäuser, Basel, 1997, see Appendix D.
3. R. Cushman, Centrum voor Wiskunde en Informatica Newsletter 1, 4 (1983); see also Chapter IV of R.H. Cushman, L.M. Bates, Global Aspects of Classical Integrable Systems, Birkhäuser, Basel, 1997.
4. R. Cushman, Centrum voor Wiskunde en Informatica Newsletter 1, 4 (1983); see also Chapter IV of R.H. Cushman, L.M. Bates, Global Aspects of Classical Integrable Systems, Birkhäuser, Basel, 1997.
5. R. Cushman, J.C. van der Meer, Lecture Notes in Mathematics, Vol. 1416, Springer, Berlin, 1991, p. 26.
6. R. Cushman, H. Knörrer, Lecture Notes in Mathematics, Vol. 1139, Springer, Berlin, 1985, p. 12.
7. J.C. van der Meer, The Hamiltonian Hopf Bifurcation, Lecture Notes in Mathematics, Vol. 1160, Springer, Berlin, 1985.
8. L. Bates, Z. Angew, Math. Phys. 6 (1991) 837.
9. M. Zou, J. Geom. Phys. 10 (1992) 37.
10. L. Bates, R. Cushman, Meccanica 30 (1995) 271.
11. R.H. Cushman, D.A. Sadovskií, Europhys. Lett. 47 (1999) 1.
12. D.A. Sadovskií, B.I. Zhilinskií, Phys. Lett. A 256 (1999) 235.
13. R. Cushman, J.J. Duistermaat, Non-Hamiltonian monodromy, Preprint, Utrecht, 1997.
14. R. Cushman, J.J. Duistermaat, Bull. Am. Math. Soc. 19 (1988) 475.
15. Vũ Ngoc San, Commun. Math. Phys. 203 (1999) 465.
16. M.S. Child, J. Phys. A 31 (1998) 657.
17. M.S. Child, T. Weston, J. Tennyson, Mol. Phys. 96 (1999) 371.
18. M. Kuwata, A. Harada, H. Hasegawa, J. Phys. A 23 (1990) 3227.
19. D. Farrelly, J. Chem. Phys. 85 (1986) 2119.
20. D. Farrelly, K. Krantzman, Phys. Rev. A 43 (1991) 1666.
21. K.D. Krantzman, J. Milligan, D. Farrelly, Phys. Rev. A 45 (1992) 3093.
22. D. Farrelly, J.A. Milligan, Phys. Rev. A 45 (1992) 8277.
23. D. Farrelly, T. Uzer, P.E. Raines, J.P. Skelton, J. Milligan, Phys. Rev. A 45 (1992) 4738.
24. D.A. Sadovskií, B.I. Zhilinskií, L. Michel, Phys. Rev. A 53 (1996) 4064.
25. D.A. Sadovskií, B.I. Zhilinskií, Phys. Rev. A 57 (1998) 2867.
26. J.C. van der Meer, R.H. Cushman, in: H. Doebner, J. Henning (Eds.), Proceedings of the XV International Conference on Diffrential Geometric Methods in Theoretical Physics, World Scientific, Singapore, 1987, p. 403.
27. R.H. Cushman, in: C. K. Jones et al. (Eds.), Dynamics Reported, Vol. 1, New Series, Springer, New York, 1992, p. 54.
28. D.A. Sadovskií, Unpublished result.
29. T. Uzer, Phys. Rev. A 42 (1990) 5787.
30. A.R.P. Rau, L. Zhang, Phys. Rev. A 42 (1990) 6342.
31. M.J. Gourlay, T. Uzer, D. Farrelly, Phys. Rev. A 47 (1993) 3113.
32. J. von Milczewski, G.H.F. Diercksen, T. Uzer, Phys. Rev. Lett. 73 (1994) 2428.
33. J. von Milczewski, G.H.F. Diercksen, T. Uzer, Int. J. Bifurc. Chaos 4 (1994) 905.
34. E. Flöthmann, J. Main, K.W. Welge, J. Phys. B 27 (1994) 2821.
35. E. Flöthmann, K.W. Welge, Phys. Rev. A 54 (1996) 1884.
36. J. von Milczewski, D. Farrelly, T. Uzer, Phys. Rev. Lett. 78 (1997) 2349.
37. J. von Milczewski, D. Farrelly, T. Uzer, Phys. Rev. A 56 (1997) 657.
38. J. von Milczewski, T. Uzer, Phys. Rev. E 55 (1997) 6540.
39. E.A. Solov'ev, Sov. Phys. JETP 58 (1983) 63.
40. R.H. Cushman, L.M. Bates, Global Aspects of Classical Integrable Systems, Birkhäuser, Basel, 1997, p. 408.
41. Nguyen Tien Zung, Diff. Geom. Appl. 7 (1997) 123.
42. R.H. Cushman, D.A. Sadovskií, Degenerate Hamiltonian Hopf bifurcation, in preparation.
43. P.A. Braun, E.A. Solov'ev, Sov. Phys. JETP 59 (1984) 38.
44. M. Robnik, J. Phys. A 17 (1984) 109.
45. M. Robnik, E. Schrüfer, J. Phys. A 18 (1985) L853.
46. R.N. Zare, Angular Momentum, Wiley, New York, 1988.
47. L.D. Landau, E.M. Lifshitz, Quantum Mechanics, Nonrelativistic Theory, Chapter XV, Section 113, Pergamon Press, Oxford, 1965.
48. E.A. Solov'ev, JETP Lett. 34 (1981) 265.
49. E.A. Solov'ev, Sov. Phys. JETP 55 (1982) 1017.
50. D.R. Herrick, Phys. Rev. A 26 (1982) 323.
51. J.B. Delos, S.K. Knudson, D.W. Noid, Phys. Rev. A 28 (1983) 7.
52. W. Gröbner, Die Lie-Reihen und ihre Anwendungen, Deutscher Verlag der Wissenschaften, Berlin, 1960.
53. W Gröbner, Contributions to the method of Lie series, Bibliographisches Institut, Mannheim, 1967.
54. A. Deprit, Celest. Mech. 1 (1969) 12.
55. A. Deprit, V. Lanchares, M. Iñarrea, J.P. Salas, J.D. Sierra, Phys. Rev. A 54 (1996) 3885.
56. J.P. Salas, A. Deprit, S. Ferrer, V. Lanchares, J. Palacián, Phys. Lett. A 242 (1998) 83.
57. B.I. Zhilinskií, L. Michel, Rydberg states of atoms and molecules. Basic group theoretical and topological analysis, Preprint IHES/P/97/54, Phys. Rep., in press.
58. H. Bateman, A. Erdélyi, Higher Transcendental Functions, Vol. 3, McGraw-Hill, New York, 1955 (Chapter 13.13).
59. M. Kummer, Fields Inst. Commun. 8 (1996) 35.
60. G. Wiebusch, J. Main, K. Kruger, H. Rottke, A. Holle, K. Welge, Phys. Rev. Lett. 62 (1989) 2821.
61. G. Reithel, H. Walther, Phys. Rev. A 49 (1993) 1646.
62. C. Neumann, R. Ubert, S. Freund, E. Flöthmann, B. Sheehy, K.H. Welge, M.R. Haggerty, J.B. Delos, Phys. Rev. Lett. 78 (1997) 4705.
63. H. Weyl, Classical Groups, their Invariants and Representations, Princeton University Press, Princeton, NJ, 1939.
64. R.P. Stanley, Invariants of finite groups and their applications to combinatorics, Bull. Am. Math. Soc. 1 (1979) 475.
65. B. Sturmfels, Algorithms in Invariant Theory, Springer, Berlin, 1993.