Institute of Mathematical Statistics Lecture Notes - Monograph Series

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

H. W. Broer, H. Hanssmann, J. Hoo, V. Naudot

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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Primary Subjects: 37J40
Secondary Subjects: 70H08
Keywords: KAM theory; quasi-periodic Hamiltonian Hopf bifurcation; singular foliation; the Lagrange top; gyroscopic stabilization
Full-text: Open access
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.lnms/1196285829
Mathematical Reviews (MathSciNet): MR2306209
Digital Object Identifier: doi:10.1214/074921706000000301

2012 © Institute of Mathematical Statistics

Institute of Mathematical Statistics Lecture Notes - Monograph Series

Institute of Mathematical Statistics Lecture Notes - Monograph Series