We study phase space transport in a 2D caldera potential energy surface (PES)
using techniques from nonlinear dynamics. The caldera PES is characterized by a
flat region or shallow minimum at its center surrounded by potential walls and
multiple symmetry related index one saddle points that allow entrance and exit
from this intermediate region.We have discovered four qualitatively distinct
cases of the structure of the phase space that govern phase space transport.
These cases are categorized according to the total energy and the stability of
the periodic orbits associated with the family of the central minimum, the
bifurcations of the same family, and the energetic accessibility of the index
one saddles. In each case we have computed the invariant manifolds of the
unstable periodic orbits of the central region of the potential and the
invariant manifolds of the unstable periodic orbits of the families of periodic
orbits associated with the index one saddles. We have found that there are
three distinct mechanisms determined by the invariant manifold structure of the
unstable periodic orbits govern the phase space transport. The first mechanism
explains the nature of the entrance of the trajectories from the region of the
low energy saddles into the caldera and how they may become trapped in the
central region of the potential. The second mechanism describes the trapping of
the trajectories that begin from the central region of the caldera, their
transport to the regions of the saddles, and the nature of their exit from the
caldera. The third mechanism describes the phase space geometry responsible for
the dynamical matching of trajectories originally proposed by Carpenter and
described in Collins et al. (2014) for the two dimensional caldera PES that we
consider.Comment: 24 pages, International Journal of Bifurcation and Chaos (in press
