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Symmetry Breaking for Compact Lie Groups
 
Michael Field University of Houston
Symmetry Breaking for Compact Lie Groups
eBook ISBN:  978-1-4704-0159-7
Product Code:  MEMO/120/574.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
Symmetry Breaking for Compact Lie Groups
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Symmetry Breaking for Compact Lie Groups
Michael Field University of Houston
eBook ISBN:  978-1-4704-0159-7
Product Code:  MEMO/120/574.E
List Price: $52.00
MAA Member Price: $46.80
AMS Member Price: $31.20
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1201996; 170 pp
    MSC: Primary 58; 14; 32; 57;

    This work comprises a general study of symmetry breaking for compact Lie groups in the context of equivariant bifurcation theory. The author starts by extending the theory developed by Field and Richardson for absolutely irreducible representations of finite groups to general irreducible representations of compact Lie groups. In particular, the author allows for branches of relative equilibria and phenomena such as the Hopf bifurcation.

    The author also presents a general theory of determinacy for irreducible Lie group actions along the lines previously described by Field in Equivariant Bifurcation Theory and Symmetry Breaking. In the main result of this work, it is shown that branching patterns for generic equivariant bifurcation problems defined on irreducible representations persist under perturbations by sufficiently high order non-equivariant terms.

    The author gives applications of this result to normal form computations yielding, for example, equivariant Hopf bifurcations and shows how normal form computations of branching and stabilities are valid when taking account of the non-normalized tail.

    Readership

    Graduate students and research mathematicians specializing in equivariant bifurcation theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Technical preliminaries and basic notations
    • 3. Branching and invariant group orbits
    • 4. Genericity theorems
    • 5. Finitely determined bifurcation problems I
    • 6. Finitely-determined bifurcation problems II
    • 7. Strong determinacy: Technical preliminaries
    • 8. Strong determinacy: $\Gamma $ finite
    • 9. Strong determinacy: $\Gamma $ compact, non-finite
    • 10. Proofs of the parametrization theorems
    • 11. An application to the equivariant Hopf bifurcation
    • Appendix A. Branches of relative equilibria
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 1201996; 170 pp
MSC: Primary 58; 14; 32; 57;

This work comprises a general study of symmetry breaking for compact Lie groups in the context of equivariant bifurcation theory. The author starts by extending the theory developed by Field and Richardson for absolutely irreducible representations of finite groups to general irreducible representations of compact Lie groups. In particular, the author allows for branches of relative equilibria and phenomena such as the Hopf bifurcation.

The author also presents a general theory of determinacy for irreducible Lie group actions along the lines previously described by Field in Equivariant Bifurcation Theory and Symmetry Breaking. In the main result of this work, it is shown that branching patterns for generic equivariant bifurcation problems defined on irreducible representations persist under perturbations by sufficiently high order non-equivariant terms.

The author gives applications of this result to normal form computations yielding, for example, equivariant Hopf bifurcations and shows how normal form computations of branching and stabilities are valid when taking account of the non-normalized tail.

Readership

Graduate students and research mathematicians specializing in equivariant bifurcation theory.

  • Chapters
  • 1. Introduction
  • 2. Technical preliminaries and basic notations
  • 3. Branching and invariant group orbits
  • 4. Genericity theorems
  • 5. Finitely determined bifurcation problems I
  • 6. Finitely-determined bifurcation problems II
  • 7. Strong determinacy: Technical preliminaries
  • 8. Strong determinacy: $\Gamma $ finite
  • 9. Strong determinacy: $\Gamma $ compact, non-finite
  • 10. Proofs of the parametrization theorems
  • 11. An application to the equivariant Hopf bifurcation
  • Appendix A. Branches of relative equilibria
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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