  We use the Reversibility Error Method and the Fidelity to analyze the global
effects of a small perturbation in a non-integrable system. Both methods have
already been proposed and used in the literature but the aim of this paper is
to compare them in a physically significant example adding some considerations
on the equivalence, observed in this case, between round-off and random
perturbations. As a paradigmatic example we adopt the restricted planar
circular three body problem. The cumulative effect of random perturbations or
round-off leads to a divergence of the perturbed orbit from the reference one.
Rather than computing the distance of the perturbed orbit from the reference
one, after a given number n of iterations, a procedure we name the Forward
Error Method (FEM), we measure the distance of the reversed orbit (n periods
forward and backward) from the initial point. This approach, that we name
Reversibility Error Method (REM), does not require the computation of the
unperturbed map. The loss of memory of the perturbed map is quantified by the
Fidelity decay rate whose computation requires a statistical average over an
invariant region.
