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

H. W. Broer, H. Hanssmann, J. Hoo, V. Naudot
2006 Institute of Mathematical Statistics Lecture Notes - Monograph Series  
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
more » ... find Cantor families of invariant isotropic tori of all dimensions suggested by the integrable approximation.
doi:10.1214/074921706000000301 fatcat:veed756yinffbcf5ovx2l53rza