  The purpose of this paper is to present a method to compute parameterizations
of invariant tori and bundles in non-autonomous quasi-periodic Hamiltonian
systems. We generalize flow map parameterization methods to the quasi-periodic
setting. To this end, we introduce the notion of fiberwise isotropic tori and
sketch definitions and results on fiberwise symplectic deformations and their
moment maps. These constructs are vital to work in a suitable setting and lead
to the proofs of magic cancellations that guarantee the existence of solutions
of cohomological equations. We apply our algorithms in the Elliptic Restricted
Three Body Problem and compute non-resonant 3-dimensional invariant tori and
their invariant bundles around the L1 point.
