The Perturbation of Hamiltonian Systems with a Non-Abelian Symmetry

The perturbation theory of non-commutatively integrable systems is revisited from the point of view of non-Abelian symmetry groups. Using a coordinate system intrinsic to the geometry of the symmetry, we generalize well-known estimates of Nekhoroshev (1977) in a class of systems having almost G-invariant Hamiltonians. These estimates are shown to have a natural interpretation in terms of momentum maps and co-adjoint orbits.