Hyperbolic decoupling of tangent space and effective dimension of   dissipative systems
  We show, using covariant Lyapunov vectors, that the tangent space of spatially-extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying "spurious" modes. The decoupling of the physical and spurious subspaces is defined by the absence of tangencies between them and found to take place generally; we find evidence in partial differential equations in one and two spatial dimensions and even in lattices of coupled maps or oscillators. We conjecture that the physical modes may constitute a local linear description of the inertial manifold at any point in the global attractor. 
Kazumasa A. Takeuchi, Hong-liu Yang, Francesco Ginelli, G\"unter   Radons, Hugues Chat\'e
nlin.CD cond-mat.stat-mech math-ph math.MP