  [GIKN] and [BBD1] propose two very different ways for building non hyperbolic
measures, [GIKN] building such a measure as the limit of periodic measures and
[BBD1] as the $\omega$-limit set of a single orbit, with a uniformly vanishing
Lyapunov exponent. The technique in [GIKN] was essentially used in a generic
setting, as the periodic orbits were built by small perturbations. It is not
known if the measures obtained by the technique in [BBD1] are accumulated by
periodic measures.
  In this paper we use a shadowing lemma from [G]:
  $\bullet$for getting the periodic orbits in [GIKN] without perturbing the
dynamics,
  $\bullet$for recovering the compact set in [BBD1] with a uniformly vanishing
Lyapunov exponent by considering the limit of periodic orbits.
  As a consequence, we prove that there exists an open and dense subset
$\mathcal{U}$ of the set of robustly transitive non-hyperbolic diffeomorphisms
far from homoclinic tangencies, such that for any $f\in\mathcal{U}$, there
exists a non-hyperbolic ergodic measure with full support and approximated by
hyperbolic periodic measures.
  We also prove that there exists an open and dense subset $\mathcal{V}$ of the
set of diffeomorphisms exhibiting a robust cycle, such that for any
$f\in\mathcal{V}$, there exists a non-hyperbolic ergodic measure approximated
by hyperbolic periodic measures.
