Spatio-temporal symmetries in S_N- and S_N * Z_2-equivariant systems

摘要

This paper investigates the spatio-temporal symmetries of periodic trajectories in dynamical systems with S_N and S_N * Z_2 symmetry. It turns out that trajectories in S_N-cquivariant systems cannot exhibit spatio-temporal symmetries beyond the trivial symmetry of all periodic orbits. More complex symmetries in the trajectories require additional constraints on the dynamics. The possibilities offered by S_N * Z_2 symmetric systems are considered and a specific S_3 * Z_2-equivariant system is investigated numerically.