Simulated annealing algorithm for finding periodic orbits of multi-electron atomic systems

We adapt the simulated annealing algorithm to the search of periodic orbits for classical multi-electron atomic systems. This is done by minimizing the nth return distance to the initial position on a Poincaré surface of section under an energy constraint. Here we give evidence of the feasibility of the method by applying it to the helium atom in the ground state for one to three spatial dimensions. We examine the structure of the dynamics and connect its organization to the periodic orbits we have found.