Diffeomorphisms satisfying the specification property

Kazuhiro Sakai, Naoya Sumi, Kenichiro Yamamoto
2010 Proceedings of the American Mathematical Society  
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 Λ of 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.
doi:10.1090/s0002-9939-09-10085-0 fatcat:lfkfukdombhvfonagaunl4lwpy