  We study Poincare recurrence of chaotic attractors for regions of finite
size. Contrary to the standard case, where the size of the recurrent regions
tends to zero, the measure is not supported anymore solely by unstable periodic
orbits inside it, but also by other special recurrent trajectories, located
outside that region. The presence of the latter leads to a deviation of the
distribution of the Poincare first return times from a Poissonian.
Consequently, by taken into account the contribution of these recurrent
trajectories, a corrected estimate of the measure can be provided. This has
wide experimental implications, as in the laboratory all returns can
exclusively be observed for regions of finite size only.

Chaotic Dynamics