Riddling of chaotic sets in periodic windows

Previous investigations of riddling have focused on the case when the dynamical invariant set in the symmetric invariant manifold of the system is a chaotic attractor. A situation expected to arise commonly in physical systems, however, is that the dynamics in the invariant manifold is in a periodic window. We argue and demonstrate that riddling can be more pervasive in this case because it can occur regardless of whether the chaotic set in the invariant manifold is transversly stable or unstable. Scaling behavior associated with this type of riddling is analyzed and is supported by numerical experiments.