The Barycenter Property for Robust and Generic Diffeomorphisms

Let f:Md→Md（d≥2） be a diffeomorphism on a compact C∞ manifold on M.If a diffeomorphism f belongs to the C1-interior of the set of all diffeomorphisms having the barycenter property,then f is Ω-stable.Moreover,if a generic diffeomorphism f has the barycenter property,then f is Ω-stable.We also apply our results to volume preserving diffeomorphisms.