Quasi-Periodic Stability of Subfamilies of an Unfolded Skew Hopf Bifurcation

In the skew Hopf bifurcation a quasi-periodic attractor with nontrivial normal linear dynamics loses hyperbolicity. The simplest setting concerns rotationally symmetric diffeomorphisms of S1×R2. Their dynamics involve periodicity, quasi-periodicity 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 sufficiently many unfolding parameters, the invariant circle persists for a large Hausdorff measure subset of a submanifold in parameter space.