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We consider a small SO(2)-equivariant perturbation of a reaction-diffusionsystem on the sphere, which is equivariant with respect to the group SO(3) ofall rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of arotating wave on the sphere that persists to a normally hyperbolicSO(2)-invariant manifold $M(\epsilon)$. We investigate the effects of thisforced symmetry breaking by studying the perturbed dynamics induced on$M(\epsilon)$ by the above reaction-diffusion system. We prove that dependingon the frequency vectors of the rotating waves that form the relativeequilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotatingwaves or SO(2)-orbits of modulated rotating waves (if some transversalityconditions hold). The orbital stability of these solutions is established aswell. Our main tools are the orbit space reduction, Poincare map and implicitfunction theorem

Forced symmetry breaking fromSO(3) toSO(2) for rotating waves on a sphere