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2009

Families of classical subgroup separable superintegrable systems

Kalnins, E. G., Kress, J. M., Miller Jr, W.

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We describe a method for determining a complete set of integrals for a classical Hamiltonian that separates in orthogonal subgroup coordinates.

As examples, we use it to determine complete sets of integrals, polynomial in the momenta, for some families of generalized oscillator and Kepler-Coulomb systems, hence demonstrating their superintegrability.
The latter generalizes recent results of Verrier and Evans, and Rodriguez, Tempesta and Winternitz.
Another example is given of a superintegrable system on a non-conformally flat space.

Families of classical subgroup separable superintegrable systems · Around

Built on

V. I. Arnold. Mathematical Methods of Classical Mechanics, (Springer, Berlin, 1989)
1989
Earlier work this paper cites.
P. Tempesta, A. Turbiner and P. Winternitz. Exact solvability of superintegrable systems J. Math. Phys
2001
Earlier work this paper cites.
E. G. Kalnins, J. M. Kress, W. Miller Jr., and G. S. Pogosyan. Complete sets of invariants for dynamical systems that admit separation of variables. J. Math. Phys
2002
Earlier work this paper cites.

Similar

E.G.Kalnins, W.Miller Jr., and G.S.Pogosyan. Exact and quasi-exact solvability of second order superintegrable quantum systems. I Euclidean space preliminaries
2006
Cited alongside, same era.
P. E. Verrier and N. W. Evans. A new superintegrable Hamiltonian. J. Math. Phys
2008
Cited alongside, same era.
F. Tremblay, V. A. Turbiner and P. Winternitz. An infinite family of solvable and integrable quantum systems on a plane. J. Phys. A: Math. Theor
2009
Cited alongside, same era.

Then

E. G. Kalnins, W. Miller Jr., and G. S. Pogosyan. Superintegrability and higher order constants for classical and quantum systems. (submitted) arXiv:0912.2278v1 [math-ph] (2009)
Original
2009
Closest in time.
M. A. Rodríguez, P. Tempesta, and P. Winternitz. Symmetry reduction and superintegrable Hamiltonian systems Journal of Physics: Conference Series
2009
Closest in time.

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