Cartan connections and momentum maps
Collective geodesic flows
We show that most compact semi-simple Lie groups carry many left invariant metrics with positive topological entropy. We also show that many homogeneous spaces admit collective Riemannian metrics arbitrarily close to the bi-invariant metric and whose geodesic flow has positive topological entropy. Other properties of collective geodesic flows are also discussed.
Convexity of Hamiltonian manifolds.
Convexity Properties of the Moment Mapping.