Quantitative characterization of complexity and predictability

Abstract The asymptotic behaviour of a generic nonlinear dynamical system F is estimated by constructing a sequence of Markov models F ( l ) 0 which approach the original system increasingly better for l →∞. 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 F ( l ) 0 . Relations between C and the convergence rate of block-entropies are discussed.