The present notes are devoted to the study of bifurcations of invariant
tori in Hamiltonian systems. Hamiltonian dynamical systems can be used
to model frictionless mechanics, in particular celestial mechanics. We are
concerned with the nearly integrable context, where Kolmogorov–Arnol’d–
Moser (KAM) theory shows that most motions are quasi-periodic whence the
(invariant) closure is a torus. An interesting aspect is that we may encounter
torus bifurcations of high co-dimension in a single given Hamiltonian system.
Historically, bifurcation theory has first been developed for dissipative dynamical
systems, where bifurcations occur only under variation of external
parameters.