Group-Theoretic Bifurcation Theory
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.
KeywordsIrreducible Representation Jacobian Matrix Unitary Representation Reciprocal System Bifurcation Equation
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