  We study a d-dimensional coupled map lattice consisting of hyperbolic toral
automorphisms (Arnold cat maps) that are weakly coupled by an analytic coupling
map. We construct the Sinai-Ruelle-Bowen measure for this system and study its
marginals on the tori. We prove they are absolutely continuous with respect to
the Lebesgue measure if and only if the coupling satisfies a nondegeneracy
condition.
