Title: Singularities and groups in bifurcation theory
First published: 1985
Description: 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.
Subjects: Group theory, Bifurcation theory, Singularity theory, Groups & group theory, Mathematics, Group Theory and Generalizations, Geometry, Global analysis (Mathematics), Analysis, Applications of Mathematics
LC classification: QA1 .A647 vol. 51, etc., QA374 .A647 vol. 51, etc.