  We used for the first time the method of periodic orbit dividing surfaces in
a non-integrable Hamiltonian system with three degrees of freedom. We have
studied the structure of these four dimensional objects in the five dimensional
phase space. This method enabled us to detect the reactive and non-reactive
trajectories in a three dimensional Caldera potential energy surface. We
distinguished four distinct types of trajectory behavior. Two of the types of
trajectories could only occur in a three dimensional Caldera potential energy
surface and not in a two dimensional surface, and we have shown that this is a
result of homoclinic intersections. These homoclinic intersections were
analyzed with the method of Lagrangian descriptors. Finally, we were able to
detect and describe the phenomenon of dynamical matching in the three
dimensional Caldera potential energy surface, which is an important mechanism
for understanding the reaction dynamics of organic molecules.
