The Quasi-Periodic Centre-Saddle Bifurcation

Nearly integrable families of Hamiltonian systems are considered in the neighbourhood of normally parabolic invariant tori. In the integrable case such tori bifurcate into normally elliptic and normally hyperbolic invariant tori. With a KAM-theoretic approach it is shown that both the normally parabolic tori and the bifurcation scenario survive a non-integrable perturbation, parametrised by pertinent large Cantor sets. These results are applied to rigid body dynamics.