Group-theoretic bifurcation theory

Kiyohiro Ikeda, Kazuo Murota

研究成果: Chapter

抄録

Group-theoretic bifurcation theory is introduced as a means to describe qualitative aspects of symmetry-breaking bifurcation, such as possible types of critical points and the symmetry of bifurcating solutions. We advance a series of mathematical concepts and tools, including: group equivariance, Liapunov–Schmidt reduction, equivariant branching lemma, and block-diagonalization. The theory of linear representations of finite groups in Chap. 7 forms a foundation of this chapter. This chapter is an extension of Chap. 2 to a system with symmetry and a prerequisite to the study of structures and materials with dihedral symmetry in Chaps. 9 – 13 and larger symmetries in Chaps. 14 – 17.

本文言語English
ホスト出版物のタイトルApplied Mathematical Sciences (Switzerland)
出版社Springer
ページ201-235
ページ数35
DOI
出版ステータスPublished - 2019 1 1

出版物シリーズ

名前Applied Mathematical Sciences (Switzerland)
149
ISSN(印刷版)0066-5452
ISSN(電子版)2196-968X

ASJC Scopus subject areas

  • 応用数学

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