Heinz Hanßmann
Perturbations of integrable and superintegrable Hamiltonian systems
(233K, PostScript)

ABSTRACT.  Integrable systems admitting a sufficiently large symmetry
group are considered. In the non-degenerate case this group is abelian
and KAM theory ensures that most of the resulting Lagrangean tori
persist under small non-integrable perturbations. For non-commutative
symmetry groups the system is superintegrable, having additional
integrals of motion that fibre Lagrangean tori into lower
dimensional invariant tori. This simplifies the integrable
dynamics, but renders the perturbation analysis more complicated.
I review important cases where it is possible to find an
`intermediate' integrable system that is non-degenerate and
approximates the perturbed dynamics.