Observing Chaos: Deducing and Tracking the State of a Chaotic System from Limited Observation

A method is proposed whereby the full state vector of a chaotic system can be reconstructed and tracked using only the time series of a single observed scalar. It is assumed that an accurate mathematical description of the system is available. Noise effects on the procedure are investigated using as an example a kicked mechanical system which results in a four-dimensional dissipative map.