Symmetry Breaking for Compact Lie Groups (Memoirs of the American Mathematical Society)

The author also presents a general theory of determinacy for irreducible Lie group actions along the lines previously described by Field in Equivariant Bifurcation Theory and Symmetry Breaking. In the main result of this work, it is shown that branching patterns for generic equivariant bifurcation problems defined on irreducible representations persist under perturbations by sufficiently high order non-equivariant terms.

The author gives applications of this result to normal form computations yielding, for example, equivariant Hopf bifurcations and shows how normal form computations of branching and stabilities are valid when taking account of the non-normalized tail.