M. Golubitsky and Ian Stewart
Hopf bifurcation in the presence of symmetry
Arch. Rational Mech. Anal. 87 No. 2 (1985) 107-165.
See also: Bull. AMS 11 No. 2 (1984) 339-342..
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: 0(2) acting on R^2, 0(n) on R^n,
and 0(3) in any irreducible representation on spherical harmonics.