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Bifurcation theory studies how the structure of solutions to equations changes as parameters are varied. Four broad topics are covered: group theory and steady-state bifurcation, equicariant singularity theory, Hopf bifurcation with symmetry, and mode interactions.
Mathematical symmetry and chaos come together to form striking, beautiful colour images throughout this impressive work, which addresses how the dynamics of complexity can produce familiar universal patterns.
The framework of 'symmetry' provides an important route between the abstract theory and experimental observations. From the reviews:"[The] rich collection of examples makes the book...extremely useful for motivation and for spreading the ideas to a large Community."--MATHEMATICAL REVIEWS
This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view.
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