Spatio-temporal symmetries in SN- and SN×2-equivariant systems

Abstract

This paper investigates the spatio-temporal symmetries of periodic trajectories in dynamical systems with SN- and SN×2 symmetry. It turns out that trajectories in SN-equivariant 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 SN×2 symmetric systems are considered and a specific S3×2-equivariant system is investigated numerically.