ABSTRACT
We say that a compact invariant set Λ of a C1-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 Λ, and there exists a C1-neighbourhood of X such that for any , the continuation ΛY of Λ for Y and U is shadowable for Yt. In this paper, we prove that any chain transitive set of a C1-vector field on M is hyperbolic if and only if it is robustly shadowable.
Acknowledgments
The authors would like to thank the referees for reading of the manuscript and useful comments. The second author was supported by the NRF grant funded by the Korea government (MSIP) (No. NRF-2015R1A2A2A01002437).
Disclosure statement
No potential conflict of interest was reported by the authors.