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We compare the divergence of orbits and the reversibility error for discretetime dynamical systems. These two quantities are used to explore the behaviorof the global error induced by round off in the computation of orbits. Thesimilarity of results found for any system we have analysed suggests the use ofthe reversibility error, whose computation is straightforward since it does notrequire the knowledge of the exact orbit, as a dynamical indicator. Thestatistics of fluctuations induced by round off for an ensemble of initialconditions has been compared with the results obtained in the case of randomperturbations. Significant differences are observed in the case of regularorbits due to the correlations of round off error, whereas the results obtainedfor the chaotic case are nearly the same. Both the reversibility error and theorbit divergence computed for the same number of iterations on the whole phasespace provide an insight on the local dynamical properties with a detailcomparable with other dynamical indicators based on variational methods such asthe finite time maximum Lyapunov characteristic exponent, the mean exponentialgrowth factor of nearby orbits and the smaller alignment index. For 2Dsymplectic maps the differentiation between regular and chaotic regions is wellfull-filled. For 4D symplectic maps the structure of the resonance web as wellas the nearby weakly chaotic regions are accurately described.

Analysis of Round Off Errors with Reversibility Test as a Dynamical Indicator