  The ultimate semiclassical wave packet propagation technique is a complex,
time-dependent WBK method known as generalized Gaussian wave packet dynamics
(GGWPD). It requires overcoming many technical difficulties in order to be
carried out fully in practice. In its place roughly twenty years ago,
linearized wave packet dynamics was generalized to methods that include sets of
off-center, real trajectories for both classically integrable and chaotic
dynamical systems that completely capture the dynamical transport. The
connections between those methods and GGWPD are developed in a way that enables
a far more practical implementation of GGWPD. The generally complex saddle
point trajectories at its foundation are found using a multi-dimensional,
Newton-Raphson root search method that begins with the set of off-center, real
trajectories. This is possible because there is a one-to-one correspondence.
The neighboring trajectories associated with each off-center, real trajectory
form a path that crosses a unique saddle; there are exceptions which are
straightforward to identify. The method is applied to the kicked rotor to
demonstrate the accuracy improvement as a function of $\hbar$ that comes with
using the saddle point trajectories.
