  Let T be an ergodic automorphism of the d-dimensional torus T^d, and f be a
continuous function from T^d to R^l. On the probability space T^d equipped with
the Lebesgue-Haar measure, we prove the weak convergence of the sequential
empirical process of the sequence (f o T^i)_{i \geq 1} under some mild
conditions on the modulus of continuity of f. The proofs are based on new limit
theorems and new inequalities for non-adapted sequences, and on new estimates
of the conditional expectations of f with respect to a natural filtration.
