Iterates of Maps with Symmetry
SIAM J. Math. Anal 19 No. 6 (1988) 423-436.
In the last sections this result is used to show that Hopf bifurcation from standing waves in a system of ordinary differential equations with 0(2) symmetry can lead directly to motion on an invariant 3-torus; indeed, depending on the exact symmetry of the standing waves, one might expect to see three invariant 3-tori emanating from such a bifurcation. The unexpected third frequency comes from drift along the torus of standing waves whose existence is forced by the 0(2) symmetry.