Formulas for the Eckmann-Ruelle Matrix

Determination of the local linearization information from experimental dynamical data is a key step in the methodology of attractor reconstruction. Because the dimension of the reconstruction space is typically higher than the original phase space dimension, some of the information in the reconstructed Jacobian, which we call the Eckmann-Ruelle matrix, reflects details of the embedding rather than the underlying dynamics. We establish formulas for the expected values of the entries of the Eckmann-Ruelle matrix, in both the presence and absence of observational noise.