On optimal coding of non-linear dynamical systems

We consider the problem of zero-delay coding of a deterministic dynamical system over a discrete noiseless channel under three estimation criteria concerned with the low-distortion regime. For these three criteria, formulated stochastically in terms of a probability distribution for the initial state, we characterize the smallest channel capacity above which the estimation objectives can be achieved. The results establish further connections between topological and metric entropy of dynamical systems and information theory.