  We study the time of $n$th return of orbits to some given (union of)
rectangle(s) of a Markov partition of an Axiom A diffeomorphism. Namely, we
prove the existence of a scaled generating function for these returns with
respect to any Gibbs measure (associated to a Holderian potential). As a
by-product, we derive precise large deviation estimates and a central limit
theorem for Birkhoff averages of Poincare cycles. We emphasize that we look at
the limiting behavior in term of number of visits (the size of the visited set
is kept fixed). Our approach relies on the spectral properties of a
one-parameter family of induced transfer operators on unstable leaves crossing
the visited set.
