Intrinsic Character of One Property of Hyperbolic Sets

The paper is devoted to the local premaximality property in the class of hyperbolic sets. (An invariant set F of a diffeomorphism S has this property, if it is not locally maximal, but in any neighborhood of F there exists a locally maximal invariant set containing F.) We prove that (in this class) the property of F to be or not to be locally premaximal depends only on the “interior dynamics” inside F, i.e. it depends only on the restriction S|F.