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

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dc.creatorBroer, H. W.
dc.creatorHanßmann, H.
dc.creatorHoo, J.
dc.creatorNaudot, V.
dc.date2006-08-10
dc.date.accessioned2026-07-07T07:21:37Z
dc.date.available2026-07-07T07:21:37Z
dc.descriptionMotivated 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.
dc.descriptionPublished at http://dx.doi.org/10.1214/074921706000000301 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0608255
dc.identifierhttp://arxiv.org/abs/math/0608255
dc.identifierIMS Lecture Notes--Monograph Series 2006, Vol. 48, 286-303
dc.identifierdoi:10.1214/074921706000000301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115365
dc.subjectDynamical Systems
dc.subject37J40 (Primary) 70H08 (Secondary)
dc.titleNearly-integrable perturbations of the Lagrange top: applications of KAM-theory
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