Embedding Theory of Dynamical Systems and Reconstructing Attractors from Data Time Series(<Special Topics>Dynamical Systems-Recent Developments in Applied Mathematics-)

Abstract

This paper reviews such embedding theorems of dynamical systems as Takens' embedding theory and the extended theory by Sauer et al. and practical methods to reconstruct possible attractors only from observed time series data. These are bases for time series analysis from the view point of nonlinear dynamical systems theory. The reconstruction method by filtered delay coordinates is also discussed.