Information content and predictability of lumped and distributed dynamical systems

We discuss several questions related to the predictability of chaotic systems. We first review the information flow through systems with few degrees of freedom and with sensitive dependence on initial conditions, and ways of measuring this flow. We then ask how the knolwedge obtained in this way can be used in improving forecasts, and propose one way of forecasting suggested by dynamical systems concepts. On the more fundamental level, we point out the difference between difficulty and possibility of forecasting, illustrating it with quadratic maps. Next, we ask ourselves how this should be generalized to distributed (i.e., spatially extended) and homogeneous systems. We point out that even the basic concepts of how information is processed by such systems are unknown. Finally, we discuss some intermittency-like effects in coupled maps and cellular automata.