  Exploring abundance and non lacunarity of hyperbolic times for endomorphisms
preserving an ergodic probability with positive Lyapunov exponents, we obtain
that there are periodic points of period growing sublinearly with respect to
the lenght of almost every dynamical ball. In particular, we conclude that any
ergodic measure with positive Lyapunov exponents satisfy the nonuniform
specification property.
  As consequences, we (re)-obtain estimates on the recurrence to a ball in
terms of the Lyapunov exponents and we prove that any expanding measure is
limit of Dirac measures on periodic points.
