  We obtain a description of the Poincar\'e recurrences of chaotic systems in
terms of the ergodic theory of transient chaos. It is based on the equivalence
between the recurrence time distribution and an escape time distribution
obtained by leaking the system and taking a special initial ensemble. This
ensemble is atypical in terms of the natural measure of the leaked system, the
conditionally invariant measure. Accordingly, for general initial ensembles,
the average recurrence and escape times are different. However, we show that
the decay rate of these distributions is always the same. Our results remain
valid for Hamiltonian systems with mixed phase space and validate a split of
the chaotic saddle in hyperbolic and non-hyperbolic components.
