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Eigenvalue Problems with the Symmetry of a Group and Bifurcations

  • B. Werner
Part of the NATO ASI Series book series (ASIC, volume 313)

Abstract

For parameter dependent nonlinear Γ-equivariant dynamical systems
$$\dot x = g(x,\lambda ),\,g:X \times IR \to X,\,X = I{R^n},$$
, along a branch of Γ-symmetric equilibria {(x(s),λ(s)) : sI} the Jacobians \( A(s): = \tfrac{{\partial g}}{{\partial x}}(x(s),\lambda (s)) \)share the Γ-equivariance with g(.,λ):
$$\gamma A(s) = A(s)\gamma \,for\,all\,\gamma \, \in \,\Gamma $$
(1.1)
.(Here Γ is a compact Lie group of orthogonal nx n-matrices).

Keywords

Irreducible Representation Hopf Bifurcation Bifurcation Point Complex Type Simple Eigenvalue 
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

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • B. Werner
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HamburgHamburg 13Federal Republic of Germany

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