  We consider some nonuniformly hyperbolic invertible dynamical systems which
are modeled by a Gibbs-Markov-Young tower. We assume a polynomial tail for the
inducing time and a polynomial control of hyperbolicity, as introduced by
Alves, Pinheiro and Azevedo. These systems admit a physical measure with
polynomial rate of mixing. In this paper we prove that the distribution of the
number of visits to a ball B(x, r) converges to a Poisson distribution as the
radius r $\to$ 0 and after suitable normalization.
