Magnetic Flows on Homogeneous Spaces
Mathematical Physics
2008-12-23 v2 Differential Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular (co)adjoint orbits of compact Lie groups. We give the proof of the non-commutative integrability of flows and show, in addition, for the case of (co)adjoint orbits, the usual Liouville integrability by means of analytic integrals. We also consider the potential systems on adjoint orbits, which are generalizations of the magnetic spherical pendulum. The complete integrability of such system is proved for an arbitrary adjoint orbit of a compact semisimple Lie group.
Cite
@article{arxiv.math-ph/0609005,
title = {Magnetic Flows on Homogeneous Spaces},
author = {Alexey V. Bolsinov and Bozidar Jovanovic},
journal= {arXiv preprint arXiv:math-ph/0609005},
year = {2008}
}
Comments
21 pages, minor changes, final version, to appear in Commentarii Mathematici Helvetici