Bifurcation theory studies how the structure of solutions to equations
changes as parameters are varied. The nature of these changes depends
both on the number of parameters and on the symmetries of the equations.
Volume I discusses how singularity-theoretic techniques aid the
understanding of transitions in multiparameter systems. This volume
focuses on bifurcation problems with symmetry and shows how
group-theoretic techniques aid the understanding of transitions in
symmetric systems. Four broad topics are covered: group theory and
steady-state bifurcation, equicariant singularity theory, Hopf
bifurcation with symmetry, and mode interactions. The opening chapter
provides an introduction to these subjects and motivates the study of
systems with symmetry. Detailed case studies illustrate how
group-theoretic methods can be used to analyze specific problems arising
in applications.