Expansive transitive sets for robust and generic diffeomorphisms.

Let <italic>f</italic> be a diffeomorphism on a compact smooth Riemannian manifold <italic>M</italic>, and let Λ be a closed <italic>f</italic>-invariant transitive subset of <italic>M</italic>. In this paper, we show that <italic>f</italic>|Λ is <italic>C</italic>1-stably expansive if and only if Λ is a hyperbolic basic set. Moreover, <italic>C</italic>1-generically, a locally maximal transitive set Λ is expansive if and only if it is a hyperbolic basic set. [ABSTRACT FROM AUTHOR]