When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation where the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the riddling bifurcation that occurs when an unstable periodic orbit embedded in the chaotic attractor, usually of low period, becomes transversely unstable. An immediate physical consequence of the riddling bifurcation is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.

• Received 6 December 1995

DOI:https://doi.org/10.1103/PhysRevLett.77.55