On the superintegrable Richelot systems

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.

💡 Research Summary

The paper introduces a new family of super‑integrable Hamiltonian systems, called the Richelot class, and demonstrates that their dynamics are intimately linked to the classical theory of hyper‑elliptic curves and Abelian integrals. For an N‑dimensional phase space with canonical coordinates ((q_i,p_i)) the authors consider Hamiltonians of the form
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