ENGLISH

Singularities and Groups in Bifurcation Theory: Volume II

By Martin Golubitsky , Ian Stewart , David G. Schaeffer (auth.)

Book information

Publisher
Springer-Verlag New York
Year
1988
ISBN
978-1-4612-8929-6, 978-1-4612-4574-2
DOI
10.1007/978-1-4612-4574-2
Language
english
Format
PDF
Filesize
21 MB (21599161 bytes)
Series
Applied Mathematical Sciences 69
Edition
1
Pages
536\551
Time added
2014-02-12 18:00:00
Group Theory and Generalizations

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.

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