  We compare the divergence of orbits and the reversibility error for discrete
time dynamical systems. These two quantities are used to explore the behavior
of the global error induced by round off in the computation of orbits. The
similarity of results found for any system we have analysed suggests the use of
the reversibility error, whose computation is straightforward since it does not
require the knowledge of the exact orbit, as a dynamical indicator. The
statistics of fluctuations induced by round off for an ensemble of initial
conditions has been compared with the results obtained in the case of random
perturbations. Significant differences are observed in the case of regular
orbits due to the correlations of round off error, whereas the results obtained
for the chaotic case are nearly the same. Both the reversibility error and the
orbit divergence computed for the same number of iterations on the whole phase
space provide an insight on the local dynamical properties with a detail
comparable with other dynamical indicators based on variational methods such as
the finite time maximum Lyapunov characteristic exponent, the mean exponential
growth factor of nearby orbits and the smaller alignment index. For 2D
symplectic maps the differentiation between regular and chaotic regions is well
full-filled. For 4D symplectic maps the structure of the resonance web as well
as the nearby weakly chaotic regions are accurately described.
