Singularities and Groups in Bifurcation Theory: Volume II (Applied Mathematical Sciences Book 69) by Martin Golubitsky (PDF)

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book provides an efficient and understandable introduction to bifurcation from fixed points in systems with symmetries. Several well established physical examples, which are the focus of active research, are discussed and further references given. It is a must for anyone interested in the subject.

⭐A very thorough and systematic description of how to treat bifurcations in equivariant dynamical systems (“systems with symmetries”).Assumes some background on bifurcation theory and group theory.Due to its unbelievably deep scope, seems more a reference book than a text for learning the subject for the first time.

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