Memoirs of the American Mathematical Society 1996; 170 pp; softcover Volume: 120 ISBN10: 0821804359 ISBN13: 9780821804353 List Price: US$52 Individual Members: US$31.20 Institutional Members: US$41.60 Order Code: MEMO/120/574
 This work comprises a general study of symmetry breaking for compact Lie groups in the context of equivariant bifurcation theory. The author starts by extending the theory developed by Field and Richardson for absolutely irreducible representations of finite groups to general irreducible representations of compact Lie groups. In particular, the author allows for branches of relative equilibria and phenomena such as the Hopf bifurcation. 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 nonequivariant 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 nonnormalized tail. Readership Graduate students and research mathematicians specializing in equivariant bifurcation theory. Table of Contents  Introduction
 Technical preliminaries and basic notations
 Branching and invariant group orbits
 Genericity theorems
 Finitely determined bifurcation problems I
 Finitelydetermined bifurcation problems II
 Strong determinacy: Technical preliminaries
 Strong determinacy: \(\Gamma\) finite
 Strong determinacy: \(\Gamma\) compact, nonfinite
 Proofs of the parametrization theorems
 An application to the equivariant Hopf bifurcation
 Branches of relative equilibria
 References
