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We use the Reversibility Error Method and the Fidelity to analyze the globaleffects of a small perturbation in a non-integrable system. Both methods havealready been proposed and used in the literature but the aim of this paper isto compare them in a physically significant example adding some considerationson the equivalence, observed in this case, between round-off and randomperturbations. As a paradigmatic example we adopt the restricted planarcircular three body problem. The cumulative effect of random perturbations orround-off leads to a divergence of the perturbed orbit from the reference one.Rather than computing the distance of the perturbed orbit from the referenceone, after a given number n of iterations, a procedure we name the ForwardError Method (FEM), we measure the distance of the reversed orbit (n periodsforward and backward) from the initial point. This approach, that we nameReversibility Error Method (REM), does not require the computation of theunperturbed map. The loss of memory of the perturbed map is quantified by theFidelity decay rate whose computation requires a statistical average over aninvariant region.

Fidelity and Reversibility in the Restricted Three Body Problem