  We investigate the statistics of recurrences to finite size intervals for
chaotic dynamical systems. We find that the typical distribution presents an
exponential decay for almost all recurrence times except for a few short times
affected by a kind of memory effect. We interpret this effect as being related
to the unstable periodic orbits inside the interval. Although it is restricted
to a few short times it changes the whole distribution of recurrences. We show
that for systems with strong mixing properties the exponential decay converges
to the Poissonian statistics when the width of the interval goes to zero.
However, we alert that special attention to the size of the interval is
required in order to guarantee that the short time memory effect is negligible
when one is interested in numerically or experimentally calculated Poincar{\'e}
recurrence time statistics.
