Archive for Rational Mechanics and Analysis

, Volume 87, Issue 2, pp 107–165 | Cite as

Hopf Bifurcation in the presence of symmetry

  • Martin Golubitsky
  • Ian Stewart


Using group theoretic techniques, we obtain a generalization of the Hopf Bifurcation Theorem to differential equations with symmetry, analogous to a static bifurcation theorem of Cicogna. We discuss the stability of the bifurcating branches, and show how group theory can often simplify stability calculations. The general theory is illustrated by three detailed examples: O(2) acting on R2, O(n) on Rn, and O(3) in any irreducible representation on spherical harmonics.


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© Springer-Verlag GmbH & Co 1985

Authors and Affiliations

  • Martin Golubitsky
    • 1
    • 2
  • Ian Stewart
    • 1
    • 2
  1. 1.Mathematics DepartmentUniversity of Houston-University ParkHouston
  2. 2.Mathematics InstituteUniversity of WarwickCoventryUK

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