  Finite entropy thermal systems undergo Poincare recurrences. In the context
of field theory, this implies that at finite temperature, timelike two-point
functions will be quasi-periodic. In this note we attempt to reproduce this
behavior using the AdS/CFT correspondence by studying the correlator of a
massive scalar field in the bulk. We evaluate the correlator by summing over
all the SL(2,Z) images of the BTZ spacetime. We show that all the terms in this
sum receive large corrections after at certain critical time, and that the
result, even if convergent, is not quasi-periodic. We present several arguments
indicating that the periodicity will be very difficult to recover without an
exact re-summation, and discuss several toy models which illustrate this.
Finally, we consider the consequences for the information paradox.
