Robustly shadowable chain transitive sets and hyperbolicity

摘要

We say that a compact invariant set A of a C~1-vector field X on a compact boundaryless Riemannian manifold M is robustly shadowable if it is locally maximal with respect to a neighbourhood U of A, and there exists a C~1-neighbourhood U of X such that for any Y∈U, the continuation Λ_Y of Λ for Y and U is shadowable for Y_t. In this paper, we prove that any chain transitive set of a C~1-vector field on M is hyperbolic if and only if it is robustly shadowable.