  The Gallavotti - Cohen Fluctuation Theorem (FT) implies an infinite set of
identities between correlation functions that can be seen as a generalization
of Green Kubo formula to the nonlinear regime. As an application, we discuss a
perturbative check of the FT relation through these identities for a simple
Anosov reversible system; we find that the lack of differentiability of the
time reversal symmetry implies a violation of the Gallavotti - Cohen
fluctuation relation. Finally, a brief comparison with Lebowitz - Spohn FT is
reported.
