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

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

2006-08-10

arxiv.org/abs/math/0608255v1

IMS Lecture Notes--Monograph Series 2006, Vol. 48, 286-303

Mathematics

Dynamical Systems

Published at http://dx.doi.org/10.1214/074921706000000301 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/

Scientific paper

10.1214/074921706000000301

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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