- 03-269 Henk W. Broer, Heinz Hanßmann, Jiangong You
- Bifurcations of Normally Parabolic Tori in Hamiltonian Systems
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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.