03-269 Henk W. Broer, Heinz Hanßmann, Jiangong You

Bifurcations of Normally Parabolic Tori in Hamiltonian Systems (302K, PostScript, gzipped and uuencoded) Jun 6, 03

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Abstract. We consider perturbations of integrable Hamiltonian systems in the neighbourhood of normally parabolic invariant tori. Under appropriate transversality conditions the tori in the unperturbed system bifurcate according to a (generalized) cuspoid catastrophe. Combining techniques of KAM-theory and singularity theory we show that such bifurcation scenarios survive the perturbation on large Cantor sets. Applications to rigid body dynamics and forced oscillators are pointed out.

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