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Bifurcation Behavior of Dn-Equivariant Systems

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

Abstract

The general framework of the group-theoretic bifurcation theory has been presented in the previous chapter. In this chapter, it is applied to the simplest group, the dihedral group D n , which represents the symmetry of the regular n-sided polygon. This is based on standard studies of the bifurcation behavior of a D n -equivariant system (Sattinger, 1979, 1983 [159], [161]; Fujii, Mimura, and Nishiura, 1982 [51]; Golubitsky, Stewart, and Schaeffer, 1988 [58]; Healey, 1985, 1988 [65], [66]; Delinitz and Werner, 1989 [37]; Ikeda, Murota, and Fujii, 1991 [91]). A few remarks are given about a system equivariant to a cyclic group C n , which has a partial symmetry of D n . While simple critical points and double bifurcation points appear inherently in D n - and C n -equivariant systems, emphasis naturally is to be placed on the double bifurcation points, because most of the results in Chapters 2 and 3 are applicable to the simple critical points of these systems.

Keywords

Irreducible Representation Bifurcation Point Dihedral Group Reciprocal System Bifurcation Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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