Drift bifurcations of relative equilibriaand transitions of spiral

We consider dynamical systems that are equivariant under a noncompact Lie group of symmetries and the drift of relative equilibria in such systems. In particular, we investigate how the drift for a parametrized family of normally hyperbolic relative equilibria can change character at what we call a `drift bifurcation'. To do this, we use results of Arnold to analyze parametrized families of elements in the Lie algebra of the symmetry group. We examine eeects in physical space of such drift bifurcations for planar reaction-diiusion systems and note that these eeects can explain certain aspects of the transition from rigidly rotating spirals to rigidly propagating`retracting waves'. This is a bifurcation observed in numerical simulations of excitable media where the rotation rate of a family of spirals slows down and gives way to a semi-innnite translating wavefront.