Diffeomorphisms satisfying the specification property

Let f be a diffeomorphism of a closed C ∞ manifold M. In this paper, we introduce the notion of the C 1 -stable specification property for a closed f-invariant set Λof M, and we prove that f/ Λ satisfies a C 1 -stable specification property if and only if Λ is a hyperbolic elementary set. As a corollary, the C 1 -interior of the set of diffeomorphisms of M satisfying the specification property is characterized as the set of transitive Anosov diffeomorphisms.