  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.
