# Magnetic flows on homogeneous spaces

### Alexey V. Bolsinov

Loughborough University, United Kingdom### Božidar Jovanović

Mathematical Institute SANU, Belgrade, Serbia

## Abstract

We consider magnetic geodesic flows of the normal metrics on a class of homogeneous spaces, in particular 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 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 this article

Alexey V. Bolsinov, Božidar Jovanović, Magnetic flows on homogeneous spaces. Comment. Math. Helv. 83 (2008), no. 3, pp. 679–700

DOI 10.4171/CMH/139