  For an ordinary thermodynamical system the Poincar\'{e} recurrence time is
exponentially large in the Boltzmann entropy of the system. It turns out, that
for a system with dynamical chaos it is determined by the Kolmogorov-Sinai
entropy and can be considerably shorter. It is shown in this note that for the
de Sitter space with strong mixing properties the mean recurrence time is equal
to the inverse Hubble constant. This means that our universe can have a finite
lifetime bounded by the current age of the universe. After this time, the
universe should recycle itself and this process has neither a beginning nor an
end.
