  In this paper we continue our studies of the two dimensional caldera
potential energy surface in a parametrized family that allows for a study of
the effect of symmetry on the phase space structures that govern how
trajectories enter, cross, and exit the region of the caldera. As a particular
form of trajectory crossing, we are able to determine the effect of symmetry
and phase space structure on dynamical matching. We show that there is a
critical value of the symmetry parameter which controls the phase space
structures responsible for the manner of crossing, interacting with the central
region (including trapping in this region) and exiting the caldera. We provide
an explanation for the existence of this critical value in terms of the
behavior of the Henon stability parameter for the associated periodic orbits.
