Integrable and Superintegrable Extensions of the Rational Calogero-Moser Model

时   间：  2022-04-14 10:00 — 12:00

We consider a class of Hamiltonian systems in 3 degrees of freedom, with a particular type of quadratic integral and which includes the rational Calogero-Moser system. We introduce separation coordinates to find the general Liouville integrable system. This gives a coupling of the Calogero-Moser system with a large class of potentials, generalising the series of potentials which are separable in parabolic coordinates. Particular cases are superintegrable, including Kepler and a resonant oscillator. Meanwhile, we study the conformally flat case and generalise all the previous results to this case. By introducing symmetry algebras of the kinetic energy, we reduce the systems from 3 to 2 degrees of freedom, giving rise to many interesting systems, including both Kepler type and Henon-Heiles type potentials on a Darboux-Koenigs $D_2$ background. This is a joint work with Allan P. Fordy.