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

1999/11/09 by Petre Dita, Dita, Petre
Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th

paper · pdf · doi:10.48550/arxiv.hep-th/9911054

Latex, 8 pages, no figures

arxiv created 1999/11/09 · arxiv updated 2009/11/30

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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