QUANTITATIVE CHARACTERIZATION OF COMPLEXITY AND PREDICTABILITY

The asymptotic behaviour of a generic nonlinear dynamical system F is estimated by constructing a sequence of Markov models F0(l) which approach the original system increasingly better for l --> infinity. The accuracy of the approximations, obtained by means of symbolic dynamical methods without assuming analytical knowledge of F itself, is evaluated by introducing a "distance" in the space of measure-preserving transformations. This quantity constitutes a measure of the complexity C of the system F, relative to the chosen approximation scheme F0(l). Relations between C and the convergence rate of block-entropies are discussed.