OPTIMAL PERIODIC-ORBITS OF CHAOTIC SYSTEMS

Invariant sets embedded in a chaotic attractor can generate time avera ges that differ from the average generated by typical orbits on the at tractor. Motivated by two different topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which i nvariant set yields the largest (optimal) value of an average of a giv en smooth function of the system state. We present numerical evidence and analysis which indicate that the optimal average is typically achi eved by a low period unstable periodic orbit embedded in the chaotic a ttractor.