On the superintegrable Richelot systems

TL;DR

This paper introduces a new class of superintegrable systems called Richelot systems, linking their integrals of motion to hyperelliptic curve theory and multiseparability in N-dimensional spaces.

Contribution

It defines the Richelot class of superintegrable systems and connects their integrability properties with classical hyperelliptic curve theory, expanding understanding of multiseparable systems.

Findings

Richelot systems are characterized by Abel equations on hyperelliptic curves.

Additional integrals of motion are quadratic in momenta.

Multiseparability relates to covers of hyperelliptic curves.

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.