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VOL. 48 | 2006 Nearly-integrable perturbations of the Lagrange top: applications of KAM-theory
J. Hoo, H. W. Broer, H. Hanssmann, V. Naudot

Editor(s) Dee Denteneer, Frank den Hollander, Evgeny Verbitskiy


Motivated by the Lagrange top coupled to an oscillator, we consider the quasi-periodic Hamiltonian Hopf bifurcation. To this end, we develop the normal linear stability theory of an invariant torus with a generic (i.e., non-semisimple) normal $1:-1$ resonance. This theory guarantees the persistence of the invariant torus in the Diophantine case and makes possible a further quasi-periodic normal form, necessary for investigation of the non-linear dynamics. As a consequence, we find Cantor families of invariant isotropic tori of all dimensions suggested by the integrable approximation.


Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1125.70003
MathSciNet: MR2306209

Digital Object Identifier: 10.1214/074921706000000301

Primary: 37J40
Secondary: 70H08

Rights: Copyright © 2006, Institute of Mathematical Statistics


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