Geodesic Flow on the n-Dimensional Ellipsoid as a Liouville Integrable System

We show that the motion on the n-dimensional ellipsoid is complete integrable by exihibiting n integrals in involution. The system is separable at classical and quantum level, the separation of classical variables being realized by the inverse of the momentum map. This system is a generic one in a new class of n-dimensional complete integrable Hamiltonians… CONTINUE READING