Embedding Theory: Introduction and Applications to Time Series Analysis

The fact that even though when we will not know the equations defining an underlying dynamical system and we are not able to measure all state space variables, we may be able to find a one-to one correspondence between the original state space and a reconstructed space using few variables means that it is possible to identify unambiguously the original state space from measurements. This has open a new field of research: non-linear time series analysis. The objective of this Chapter is to provide the reader with an overall picture of the embedding theory and time-delay state space reconstruction techniques. We hope that this introductory chapter will guide the reader in understanding the subsequent chapters where different relevant aspects of dynamical systems theory are going to be discussed in more depth and detail.