  We numerically study two conservative two-dimensional maps, namely the baker
map (whose Lyapunov exponent is known to be positive), and a typical one
(exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift
family of maps introduced by C. Moore [Phys Rev Lett {\bf 64}, 2354 (1990)] in
the context of undecidability. We calculated the time evolution of the entropy
$S_q \equiv \frac{1-\sum_{i=1}^Wp_i^q}{q-1}$ ($S_1=S_{BG}\equiv
-\sum_{i=1}^Wp_i \ln p_i$), and exhibited the dramatic effect introduced by
numerical precision. Indeed, in spite of being area-preserving maps, they
present, {\it well after} the initially concentrated ensemble has spread
virtually all over the phase space, unexpected {\it pseudo-attractors}
(fixed-point like for the baker map, and more complex structures for the Moore
map). These pseudo-attractors, and the apparent time (partial) reversibility
they provoke, gradually disappear for increasingly large precision. In the case
of the Moore map, they are related to zero Lebesgue-measure effects associated
with the frontiers existing in the definition of the map. In addition to the
above, and consistently with the results by V. Latora and M. Baranger [Phys.
Rev. Lett. {\bf 82}, 520 (1999)], we find that the rate of the
far-from-equilibrium entropy production of baker map, numerically coincides
with the standard Kolmogorov-Sinai entropy of this strongly chaotic system.
