  We prove, for f a partially hyperbolic diffeomorphism with center dimension
one, two results about the integrability of its central bundle. On one side, we
show that if the non wandering set of f is the whole manifold, and the manifold
is 3 dimensional, then the absence of periodic points implies the unique
integrability of the central bundle. On the opposite side, we prove that any
periodic point p of large period n has an f n invariant center manifold,
everywhere tangent to the center bundle. We also obtain, as a consequence of
the last result, that there is an open and dense subset of C 1 robustly
transitive and partially hyperbolic diffeomorphisms with center dimension one,
such that either the strong stable or the strong unstable foliation is minimal.
This generalizes a result obtained in BDU for 3 dimensional manifolds to any
dimension.
