Bifurcation behavior of Dn-equivariant systems

Kiyohiro Ikeda, Kazuo Murota

Research output: Chapter in Book/Report/Conference proceedingChapter


Group-theoretic bifurcation theory presented in Chap. 8 is applied to systems with dihedral group symmetry. The perfect and imperfect bifurcation behaviors of such systems in the neighborhood of bifurcation points are investigated using bifurcation equations. A hierarchy of subgroups expressing recursive bifurcation is obtained. Chapter 7 gives fundamentals of group and group representation employed herein. This chapter is a prerequisite for Chaps. 10 – 13 that deal with perfect and imperfect bifurcations of such systems.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
Number of pages59
Publication statusPublished - 2019

Publication series

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


  • Bifurcation
  • Bifurcation equation
  • Cyclic group
  • Dihedral group
  • Double bifurcation point
  • Group equivariance
  • Imperfection
  • Liapunov–Schmidt reduction
  • Recursive bifurcation
  • Symmetry

ASJC Scopus subject areas

  • Applied Mathematics


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