Bifurcation From Group Orbits

Abstract

In this chapter we address two issues. The first concerns the relation between bifurcating states in phase space and experimental observations in physical space. The second issue is that of bifurcation from group orbits. In equivariant dynamics, all states occur as entire group orbits, and especially when the group has a nontrivial continuous part — that is, when it is not finite — the fact that a group orbit is a manifold has a substantial effect on possible bifurcations. The situation becomes even more complicated — and interesting — when the symmetry group is the Euclidean group, which is not compact.