On the superintegrable Richelot systems
arXiv:0909.2923 · doi:10.1088/1751-8113/43/5/055201
Abstract
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.
13 pages, a talk given at the Conference "Symmetry Methods in Physics" devoted to the memory of Professor Y.F.Smirnov, July 6-9, 2009
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