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

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

IMS Lecture Notes Monogr. Ser., 2006: >286-303 (2006) DOI: 10.1214/074921706000000301

## 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.

## Information

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

zbMATH: 1125.70003
MathSciNet: MR2306209

Digital Object Identifier: 10.1214/074921706000000301

Subjects:
Primary: 37J40
Secondary: 70H08

Keywords: gyroscopic stabilization , KAM theory , quasi-periodic Hamiltonian Hopf bifurcation , singular foliation , the Lagrange top