Addition theorems and the Drach superintegrable systems

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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18 pages, the talk given on the conference "Superintegrable Systems in Classical and Quantum Mechanics", Prague 2008

Scientific paper

10.1088/1751-8113/41/33/335204

We propose new construction of the polynomial integrals of motion related to
the addition theorems. As an example we reconstruct Drach systems and get some
new two-dimensional superintegrable Stackel systems with third, fifth and
seventh order integrals of motion.

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