According to Takens' embedding theorem, almost all dynamical systems can be reconstructed from just one noiseless observation sequence. Unfortunately such observations of real life systems are very hard to get. There is always some measurement noise and even if that could be eliminated, the results must be stored into a computer with finite precision to do any practical calculations with them.
In practice the observation noise can be a serious hinder to the reconstruction. Low dimensional observations from a high dimensional chaotic system with high noise level can easily become indistinguishable from a random time series.