On the Drach superintegrable systems

Details On the Drach superintegrable systems On the Drach superintegrable systems

2000-01-25

arxiv.org/abs/nlin/0001053v1

J. Phys. A, Math. Gen. 33, No.41, 7407-7422, (2000)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages, Latex2e+Amssymb

Scientific paper

10.1088/0305-4470/33/41/310

Cubic invariants for two-dimensional degenerate Hamiltonian systems are considered by using variables of separation of the associated St\"ackel problems with quadratic integrals of motion. For the superintegrable St\"ackel systems the cubic invariant is shown to admit new algebro-geometric representation that is far more elementary than the all the known representations in physical variables. A complete list of all known systems on the plane which admit a cubic invariant is discussed.

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