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Nearly-integrable perturbations of the Lagrange top: applications of KAM-theory

H. W. Broer·H. Hanßmann·J. Hoo·V. Naudot
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Abstract

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.

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H. W. Broer, H. Hanßmann, J. Hoo, V. Naudot. 2006-08-10. Nearly-integrable perturbations of the Lagrange top: applications of KAM-theory. https://doi.org/10.1214/074921706000000301

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