Group-Theoretic Bifurcation Theory

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter


Qualitative aspects of symmetry-breaking bifurcation can be described by grouptheoretic bifurcation theory. In view of 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 investigated thoroughly by the Liapunov–Schmidt reduction. An extremely important finding of this theory is that the mechanism of such bifurcation does not depend on individual material or physical properties but on the symmetry of the system under consideration.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages48
Publication statusPublished - 2010

Publication series

NameApplied Mathematical Sciences (Switzerland)
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X


  • Invariant Subspace
  • Irreducible Representation
  • Jacobian Matrix
  • Reciprocal System
  • Unitary Representation

ASJC Scopus subject areas

  • Applied Mathematics


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