  In order to simulate observational and experimental situations, we consider a
leak in the phase space of a chaotic dynamical system. We obtain an expression
for the escape rate of the survival probability applying the theory of
transient chaos. This expression improves previous estimates based on the
properties of the closed system and explains dependencies on the position and
size of the leak and on the initial ensemble. With a subtle choice of the
initial ensemble, we obtain an equivalence to the classical problem of Poincare
recurrences in closed systems, which is treated in the same framework. Finally,
we show how our results apply to weakly chaotic systems and justify a split of
the invariant saddle in hyperbolic and nonhyperbolic components, related,
respectively, to the intermediate exponential and asymptotic power-law decays
of the survival probability.
