New Aspects in Bifurcation with Symmetry

Abstract

It comes as no surprise that the literature devoted to bifurcation problems involving symmetry draws from both analysis and group theory. However, it is more accurate to say that it draws from both analysis and group representation theory, the two being related through the notion of isotropy subgroup. Isotropy subgroups have been crucial to every work having some connection with bifurcation and symmetry. It is the aim of this paper to show that there are connections between bifurcation problems and group theory that do not refer to isotropy subgroups and are virtually representation-independent. In particular, it will be shown that Lie groups, including finite ones, possess subgroups of a special type, here called intrinsic isotropy subgroups, characterized by a representation-independent property, which play a role in bifurcation problems.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1989
Accession Number
ADA216506

Entities

People

  • Patrick J. Rabier

Organizations

  • University of Pittsburgh

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Banach Space
  • Covariance
  • Data Science
  • Decomposition
  • Eigenvalues
  • Equations
  • Hilbert Space
  • Identities
  • Information Science
  • Lie Groups
  • Linear Algebra
  • Mathematics
  • Military Research
  • Notation
  • Standards
  • Symmetry
  • Yield

Fields of Study

  • Mathematics

Readers

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  • Materials Science and Engineering.
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