to those of the original state space (More exactly, they are related by a smooth, invertible change of coordinates, or diffeomorphism.) The magic embedding dimension is at most , and often less. See also Whitney embedding theorem Nonlinear dimensionality reduction References Further reading External links Attractor Reconstruction (scholarpedia) Scientio's ChaosKit product uses embedding to create analyses and predictions. Access is provided online via a web service and graphic interface. Theorems in dynamical systems