RIDDLING BIFURCATION IN CHAOTIC DYNAMICAL-SYSTEMS

When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation wh ere the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the rid dling 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 bifurcati on is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.