Phase space representation

  Deterministic dynamical systems describe the time evolution of a system in some phase space . They can be expressed for example by ordinary differential equations
 
or in discrete time by maps of the form
 
A time series can then be thought of as a sequence of observations performed with some measurement function . Since the (usually scalar) sequence in itself does not properly represent the (multidimensional) phase space of the dynamical system, one has to employ some technique to unfold the multidimensional structure using the available data.

 
• Delay coordinates
• Embedding parameters
  • Mutual information
  • False nearest neighbors
• Principal components
• Poincaré sections
• SVD filters