Group-Theoretic Bifurcation Theory

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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)
PublisherSpringer
Pages151-198
Number of pages48
DOIs
Publication statusPublished - 2010

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume149
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Group-Theoretic Bifurcation Theory'. Together they form a unique fingerprint.

Cite this