Group-Theoretic Bifurcation Theory

  • Kiyohiro Ikeda
  • Kazuo Murota
Part of the Applied Mathematical Sciences book series (AMS, volume 149)


The qualitative aspects of symmetry-breaking bifurcation can be described successfully by group-theoretic bifurcation theory. With reference to the symmetry of the system under consideration, possible critical points and bifurcated solutions can be classified, and the behavior of these solutions in a neighborhood of each critical point can be thoroughly investigated by the Liapunov—Schmidt reduction. One of the most important findings of this theory is that the rule of such bifurcation does not depend on the individual material or physical properties but merely on the symmetry of the system under consideration.


Irreducible Representation Jacobian Matrix Unitary Representation Reciprocal System Bifurcation Equation 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Kiyohiro Ikeda
    • 1
  • Kazuo Murota
    • 2
  1. 1.Department of Civil EngineeringTohoku UniversityAoba SendaiJapan
  2. 2.Department of Mathematical InformaticsUniversity of TokyoTokyoJapan

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