05-88 Heinz Hanßmann

Perturbations of integrable and superintegrable Hamiltonian systems (233K, PostScript) Mar 1, 05

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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.

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