Hopf Bifurcation in the presence of symmetry
- Cite this article as:
- Golubitsky, M. & Stewart, I. Arch. Rational Mech. Anal. (1985) 87: 107. doi:10.1007/BF00280698
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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.