14-87 Heinz Hanßmann

Perturbations of superintegrable systems (987K, PostScript) Dec 19, 14

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Abstract. A superintegrable system has more integrals of motion than degrees d of freedom. The quasi-periodic motions then spin around tori of dimension n<d. Already under integrable perturbations almost all n-tori will break up; in the non-degenerate case the resulting d-tori have n fast and d-n slow frequencies. Such d-parameter families of d-tori do survive Hamiltonian perturbations as Cantor families of d-tori. A perturbation of a superintegrable system that admits a better approximation by a non-degenerate integrable perturbation of the superintegrable system is said to remove the degeneracy. In the minimal case d=n+1 this can be achieved by means of averaging, but the more integrals of motion the superintegrable system admits the more difficult becomes the perturbation analysis.

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