Quasi-Periodic Stability of Subfamilies of an unfolded skew Hopf bifurcation

In the skew Hopf bifurcation a quasi-periodic attractor with nontrivial nor mal linear dynamics loses hyperbolicity. The simplest setting concerns rota tionally symmetric diffeomorphisms of S-1 x R-2. Their dynamics involve per iodicity, quasiperiodicity and chaos, including mixed spectrum. The present paper deals with the persistence under symmetry-breaking of quasi-periodic invariant circles in this bifurcation. It turns out that, when adding suff iciently many unfolding parameters, the invariant circle persists for a lar ge Hausdorff measure subset of a submanifold in parameter space.