  In dissipative dynamical systems phase space volumes contract, on average.
Therefore, the invariant measure on the attractor is singular with respect to
the Lebesgue measure. As noted by Ruelle, a generic perturbation pushes the
state out of the attractor, hence the statistical features of the perturbation
and, in particular, of the relaxation, cannot be understood solely in terms of
the unperturbed dynamics on the attractor. This remark seems to seriously limit
the applicability of the standard fluctuation dissipation procedure in the
statistical mechanics of nonequilibrium (dissipative) systems. In this paper we
show that the singular character of the steady state does not constitute a
serious limitation in the case of systems with many degrees of freedom. The
reason is that one typically deals with projected dynamics, and these are
associated with regular probability distributions in the corresponding lower
dimensional spaces.
