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.
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