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

Petre Dita

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arXiv · hep-th/9911054

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

Petre Dita

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Abstract

We show that the motion on the n-dimensional ellipsoid is complete integrable by exhibiting 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 defined by an arbitrary function f(q,p) invertible with respect to momentum p and rational in the coordinate q.

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Petre Dita. 1999-11-09. Geodesic Flow on the n-Dimensional Ellipsoid as a Liouville Integrable System. https://arxiv.org/abs/hep-th/9911054

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