Statistical decomposition of chaotic attractors by the eigenvectors of Oseledec matrix-active and passive information dynamics

Abstract

Correlated sets of physical variables or coordinates of the equations of motion are extracted from the distribution of eigenvectors of theOseledec matrix. These coordinates characterize the dynamics on the (un-)stable manifolds. The information-theoretic properties of the dynamics on the (un-)stable foliations imply a decomposition of chaos by theactive andpassive coordinates. We introduceinformation consumption in the active dynamics to account for the complicated dynamics on some of the stable manifolds. The information flow direction is transversal to the subspace spanned by the passive coordinates. Its dynamics can beisolated orone-way decorrelated. An example is given to show how these ideas can be applied to better understand the chaotic modal interaction of a nonlinear beam.