  What is the ergodic behaviour of numerically computed segments of orbits of a
diffeomorphism? In this paper, we try to answer this question for a generic
conservative $C^1$-diffeomorphism, and segments of orbits of Baire-generic
points. The numerical truncation will be modelled by a spatial discretization.
Our main result states that the uniform measures on the computed segments of
orbits, starting from a generic point, accumulates on the whole set of measures
that are invariant under the diffeomorphism. In particular, unlike what could
be expected naively, such numerical experiments do not see the physical
measures (or more precisely, cannot distinguish physical measures from the
other invariant measures).
