The paper deals with different kinds of invariant motions (periodic orbits, 2D
and 3D invariant tori and invariant manifolds of periodic orbits) in order to analyze
the Hamiltonian direct Hopf bifurcation that takes place close to the Lyapunov
vertical family of periodic orbits of the triangular equilibrium point L4 in the 3D
restricted three-body problem (RTBP) for the mass parameter, µ, greater than
(and close to) µR (Routh’s mass parameter). Consequences of such bifurcation,
concerning the confinement of the motion close to the hyperbolic orbits and the 3D
nearby tori are also described