On the superintegrable Richelot systems

Details On the superintegrable Richelot systems On the superintegrable Richelot systems

2009-09-16

arxiv.org/abs/0909.2923v1

Journal of Physics A: Math. Theor. v. 43, 055201 (14pp), 2010

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, a talk given at the Conference "Symmetry Methods in Physics" devoted to the memory of Professor Y.F.Smirnov, July 6-

Scientific paper

10.1088/1751-8113/43/5/055201

We introduce the Richelot class of superintegrable systems in N-dimensions whose n<=N equations of motion coincide with the Abel equations on n-1 genus hyperellipic curve. The corresponding additional integrals of motion are the second order polynomials of momenta and multiseparability of the Richelot superintegrable systems is related with classical theory of covers of the hyperelliptic curves.

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