Superintegrable systems on the two-dimensional sphere S2 and the hyperbolic plane H2

Journal of Mathematical Physics

Volumn 40, Issue 10, 1999, Pages 5026-5057

  Rañada, Manuel F ^a   Santander, Mariano ^b  

^a UNIVERSITY OF ZARAGOZA   (Spain)

^b UNIVERSITY OF VALLADOLID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033211778     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533014     Document Type: Article

References (29)

1. M. Henon. "Numerical exploration of Hamiltonian systems" in Chaotic Behaviour of Deterministic Systems, edited by G. Iooss, R. H. Helleman, and R. Stora (North-Holland, Amsterdam, 1983).
2. T. I. Fris, V. Mandrosov, Y. A. Smorodinsky. M. Uhlir, and P. Winternitz, Phys. Lett. 16, 354 (1965).
3. A. A. Makarov, Y. A. Smorodinsky, K. Valiev, and P. Winternitz, Nuovo Cimento 52, 1061 (1967).
4. S. Wojciechowski, Phys. Lett. A 95, 279 (1983).
5. L. Chetouani, L. Guechi, and T. F. Hammann, Phys. Lett. A 125, 277 (1987).
6. M. V. Carpio-Bernido and C. C. Bernido, Phys. Lett. A 134, 395 (1987).
7. J. Hietarinta, Phys. Rep. 147, 87 (1987).
8. M. Kibler, and P. Winternitz, Phys. Lett. A 147, 338 (1990).
9. N. W. Evans, Phys. Rev. A 41, 5666 (1990).
10. N. W. Evans, Phys. Lett. A 147, 483 (1990).
11. N. W. Evans, J. Math. Phys. 32, 3369 (1991).
12. M. A. del Olmo, M. A. Rodríguez, and P. Winternitz, J. Math. Phys. 34, 5118 (1993).
13. J. A. Calzada, M. A. del Olmo, and M. A. Rodríguez, J. Geom. Phys. 23, 14 (1997).
14. C. Grosche, G. S. Pogosyan, and A. N. Sissakian, Fortschr. Phys. 43, 453 (1995).
15. C. Grosche, G. S. Pogosyan, and A. N. Sissakian, Fortschr. Phys. 43, 523 (1995).
16. C. Grosche, G. S. Pogosyan, and A. N. Sissakian, Phys. Part. Nuclei 27, 244 (1996).
17. E. G. Kalnins, W. Miller, Jr., and G. S. Pogosyan, J. Math. Phys. 37, 6439 (1996).
18. E. G. Kalnins, W. Miller, Jr., and G. S. Pogosyan, J. Math. Phys. 37, 5416 (1997).
19. A. L. Salas-Brito, H. N. Núñez-Yépez, and R. P. Martínez-Romero, Int. J. Mod. Phys. 12, 271 (1997).
20. M. F. Rañada, J. Math. Phys. 38, 4165 (1997).
21. C. Gonera, J. Phys. A 31, 4465 (1998).
22. M. F. Rañada, J. Math. Phys. 40, 236 (1999).
23. C. López, E. Martínez, and M. F. Rañada, "Dynamical symmetries, non-Cartan symmetries, and superintegrability of the n-dimensional harmonic oscillator,"' J. Phys. A 32, 1241 (1999).
24. D. M. Fradkin, Am. J. Phys. 33, 207 (1965).
25. E. Schroedinger, Proc. R. Ir. Acad. Sect. A. Math. Astron. Phys. Sci. A XLVI, 9 (1940).
26. P. W. Higgs, J. Phys. A 12, 309 (1979).
27. H. I. Leemon, J. Phys. A 12, 489 (1979).
28. W. Klinberger, A Course in Differential Geometry (Springer. Graduate texts in Mathematics, New York, 1978).
29. A. M. Perelomov, Integrable Systems of Classical Mechanics and Lie Algebras (Birkhauser, Basel, 1990).