Dynamical symmetries, non-Cartan symmetries and superintegrability of the n-dimensional harmonic oscillator

Journal of Physics A: Mathematical and General

Volumn 32, Issue 7, 1999, Pages 1241-1249

  López, Carlos ^a   Martínez, Eduardo ^a   Rańada, Manuel F ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039835161     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/32/7/013     Document Type: Article

References (28)

1. Henon M 1983 Numerical exploration of Hamiltonian systems Chaotic Behaviour of Deterministic Systems ed G Iooss, R H Helleman and R Stora (Amsterdam: North-Holland)
2. Fris T I, Mandrosov V, Smorodinsky Y A, Uhlir M and Winternitz P 1965 Phys. Lett. 16 354-6
3. Makarov A A, Smorodinsky Y A, Valiev K and Winternitz P 1967 Nuovo Cimento 52 1061-84
4. Wojciechowski S 1983 Phys. Lett. A 95 279-81
5. Chetouani L, Guechi L and Hammann T F 1987 Phys. Lett. A 125 277-81
6. Carpio-Bernido M V and Bernido C C 1987 Phys. Lett. A 134 395-9
7. Hietarinta J 1987 Phys. Rep. 147 87-154
8. Perelomov A M 1990 Integrable Systems of Classical Mechanics and Lie Algebras (Basle: Birkhäuser)
9. Kibler M and Winternitz P 1990 Phys. Lett. A 147 338-42
10. Evans N W 1990 Phys. Rev. A 41 5666-76
11. Evans N W 1990 Phys. Lett. A 147 483-6
12. Evans N W 1991 J. Math. Phys. 32 3369-75
13. del Olmo M A, Rodríguez M A and Winternitz P 1993 J. Math. Phys. 34 5118-39
14. del Olmo M A, Rodríguez M A and Winternitz P 1996 Fortschr. Phys. 44 199-233
15. Calzada J A, del Olmo M A and Rodríguez M A 1997 J. Geom. Phys. 23 14-30
16. Grosche C, Pogosyan G S and Sissakian A N 1995 Fortschr. Phys. 43 453-521
17. Grosche C, Pogosyan G S and Sissakian AN 1995 Fortschr. Phys. 43 523-63
18. Salas-Brito A L, Nún̈ez-Yépez H N and Martínez-Romero R P 1997 Int. J. Modern Phys. 12 271-6
19. Rañada M F 1997 J. Math. Phys. 38 4165-78
20. Gonera C 1998 J. Phys. A 31 4465-72
21. Rañada M F 1999 Superintegrability of the Calogero-Moser system: Constants of motion, master symmetries, and time-dependent symmetries J. Math. Phys. to be published
22. Tabor M 1989 Chaos and Integrability in Nonlinear Dynamics (New York: Wiley)
23. Fradkin D M 1965 Am. J. Phys. 33 207-11
24. Abraham R and Marsden J 1978 Foundations of Mechanics (Reading, MA: Benjamin)
25. Marmo G, Saletan E J, Simoni A and Vitale B 1985 Dynamical Systems: A Differential Geometric Approach (Chichester: Wiley)
26. Libermann P and Marle C M 1987 Symplectic Geometry and Analytical Mechanics (Dordrecht: Reidel)
27. de León M and Rodrigues P R 1989 Methods of Differential Geometry in Analytical Mechanics (Amsterdam: North-Holland)
28. Crampin M 1983 J. Phys. A: Math. Gen. 16 3755-72