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