A method to find unstable periodic orbits for the diamagnetic Kepler problem

A method to determine the admissibility of symbolic sequences and to find t he unstable periodic orbits corresponding to allowed symbolic sequences for the diamagnetic Kepler problem is proposed by using the ordering of stable and unstable manifolds. By investigating the unstable periodic orbits up t o length 6, a one to one correspondence between the unstable periodic orbit s and their corresponding symbolic sequences is shown under the system symm etry decomposition.