SHADOWING AND ITERATIVE INTERPOLATION FOR CEBYSEV MIXING TRANSFORMATIONS

The iteration of Čebyšev polynomials generates mixing transformations that model canonical features of chaotic systems: These include pseudo-random evolution, ergodicity, fading memory, and the irreversible dispersal of any set of positive measure throughout the mixing region. Mixing processes are also analytically and numerically unstable. Nevertheless, iterative interpolation, or numerical retrodiction, demonstrates that the computer generated trajectories are shadowed within strict error bounds by exact Čebyšev iterates. Pervasive shadowing is, however, not sufficient to ensure a generic correspondence between computer simulations and "true dynamics." This latitude is illustrated by several basic distinctions between the computer generated orbit structures and the exact analytic orbits of the Čebyšev mixing transformations. © 1992.