By focusing attention on close returns of a trajectory to itself, the existence of deterministic dynamics underlying a time series can be detected even in very short data sets. This provides a practical means of detecting determinism in moderate-dimensional (e.g. ß 7) noisy systems, or low-dimensional systems with large Lyapunov exponents such as computer random number generators. A large variety of methods have been developed to reconstruct dynamics from measured time series, and to characterize dynamics in terms of predictability or dynamical invariants such as the correlation dimension or spectrum of Lyapunov exponents. These characterizations are often applied to experimental or field time series in order to decide whether the data are consistent with a low-dimensional deterministic mechanism, or a stochastic (or extremely high-dimensional, hence, effectively stochastic) mechanism. Limits on the power of these methods arise from finite and often small lengths of data sets and measu...