Towards complete detection of unstable periodic orbits in chaotic systems

We present a rigorous analysis and numerical evidence indicating that a rec ently developed methodology for detecting unstable periodic orbits is capab le of yielding all orbits up to periods limited only by the computer precis ion. In particular, we argue that an efficient convergence to every periodi c orbit can be achieved and the basin of attraction can be made finite and accessible for typical or particularly chosen initial conditions. (C) 2001 Elsevier Science B.V. All rights reserved.