ROBUST HETEROCLINIC CYCLES

One phenomenon in the dynamics of differential equations which does no t typically occur in systems without symmetry is heteroclinic cycles. In symmetric systems, cycles can be robust for symmetry-preserving per turbations and stable. Cycles have been observed in a number of simula tions and experiments, for example in rotating convection between two plates and for turbulent flows in a boundary layer. Theoretically the existence of robust cycles has been proved in the unfoldings of some l ow codimension bifurcations and in the context of forced symmetry brea king from a larger to a smaller symmetry group. Tn this article we rev iew the theoretical and the applied research on robust cycles.