STATISTICAL DECOMPOSITION OF CHAOTIC ATTRACTORS BY THE EIGENVECTORS OF OSELEDEC MATRIX - ACTIVE AND PASSIVE INFORMATION DYNAMICS

Correlated sets of physical variables or coordinates of the equations of motion are extracted from the distribution of eigenvectors of the O seledec matrix. These coordinates characterize the dynamics on the (un -)stable manifolds. The information-theoretic properties of the dynami cs on the (un-)stable foliations imply a decomposition of chaos by the active and passive coordinates. We introduce information consumption in the active dynamics to account for the complicated dynamics on some of the stable manifolds. The information flow direction is transversa l to the subspace spanned by the passive coordinates. Its dynamics can be isolated or one-way decorrelated. An example is given to show how these ideas can be applied to better understand the chaotic modal inte raction of a nonlinear beam.