ABSTRACT
This chapter looks more closely at some low dimensional examples of equivariant bifurcations. In contrast to what happens for non-equivariant static bifurcations, one should see that periodic, even chaotic, phenomena can appear in generic static equivariant bifurcations. The chapter describes the example of Guckenheimer and Holmes, in part because it provides a good application of the invariant sphere theorem. It investigates some of the dynamics that can be generated at the bifurcation point. The chapter seems worthwhile attempting a more precise—though undoubtedly provisional—definition of a heteroclinic cycle. Essentially, a heteroclinic cycle will be a cycle of connections between flow-invariant sets.
