Driving trajectories in chaotic systems

This work presents the main ideas and the fundamental procedures for guidin g trajectories on chaotic systems and for stabilizing chaotic orbits, all w ith the use of small perturbations. We consider an extension of the Ott-Gre bogi-Yorke method of controlling chaos and an associated procedure for guid ing trajectories on chaotic sets of high dimensional systems. We argue that those techniques can be used even if the chaotic invariant set is nonattra ctive. As nonattractive chaotic invariant sets commonly exist embedded in h igh dimensional systems, we also argue that we can combine chaotic control techniques with system control strategies to generate a powerful mechanism for manipulating the dynamics. We present an example in which we change and alter system's evolution at will using only small perturbations to some ac cessible parameter.