Dynamics, Bifurcations, Symmetry (P. Chossat ed.) Kluwer, The Netherlands, 1994, 241-257
We describe some recent results on symmetry of attractors for dynamical systems with symmetry and consider the implications for the Couette-Taylor experiment and the Faraday surface wave experiment. In particular, we explore the relationship between symmetry of solutions at a fixed instant in time, and symmetry in the time-averaged solution. This leads to predictions that are somewhat surprising and which we believe require careful experimental exploration.