Drift bifurcations of relative equilibria and transitions of spiral waves

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 e ects in physical space of such drift bifurcations for planar reaction di usion systems and note that these e ects 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 in nite translating wavefront Appeared Nonlinearity