SHADOWABLE WEAKLY TRANSITIVE SETS ARE HYPERBOLIC
M. Lee · International Journal of Pure and Apllied Mathematics · 2017
Let M d (d ≥ 2) be a closed smooth manifold, and let f be a diffeomorphism on M. Let Λ be a weakly transitive set for f .First, we show that f has the C 1 -stably shadowing property on Λ if and only if Λ is a hyperbolic basic set.Finally, we prove that for C 1 -generic f, a locally maximal weakly transitive set is shadowable if and only if that weakly transitive set is a hyperbolic basic set.