  We show, using covariant Lyapunov vectors, that the chaotic solutions of
spatially extended dissipative systems evolve within a manifold spanned by a
finite number of physical modes hyperbolically isolated from a set of residual
degrees of freedom, themselves individually isolated from each other. In the
context of dissipative partial differential equations, our results imply that a
faithful numerical integration needs to incorporate at least all physical modes
and that increasing the resolution merely increases the number of isolated
modes.
