Reconstructing Dynamical Systems Driven by External Events Jaroslav Stark, Centre for Nonlinear Dynamics and its Applications, University College London, Gower Street, London, WC1E 6BT. Historically, the vast majority of the theory of nonlinear dynamical systems was developed under the assumption that one knew the state space and evolution equations of the system under consideration. In principle the application of these results to real problems thus required the simultaneous observation of all the state space variables. This is obviously not possible in many practical applications, where all that one can manage to do is to make a sequence of repeated measurements of one or more observables, whose relationship to the state variables is at best uncertain. It is then of fundamental importance to understand how much information about the original dynamical system can be extracted from such a time series. In the case of autonomous systems there exists a well developed theoretical framework for addressing this question. This is based on Takens Embedding Theorem which typically allows us to reconstruct the dynamics of an unknown system from a scalar time series generated by that system. Over the last two decades, this has led to a wide variety of new techniques for the analysis and manipulation of such time series, including algorithms for the measurement of fractal dimensions and Liapunov exponents, for the prediction of future behaviour, for noise reduction and signal separation, and most recently for control and targeting. Unfortunately, few systems in the real world are genuinely autonomous, but are rather subject to a variety of external influences including both regular and irregular forcing, stochastic effects, input of external data (e.g. communications systems), irregular sampling and so on. In such a situation, Takens Theorem does not apply and hence although many of the usual algorithms are still employed, they lack the theoretical justification which they possess in the autonomous case. In this talk, we outline a new framework for the study of such non-autonomous systems, state appropriate generalizations of Takens Theorem and discuss their relevance to practical signal processing methods.