Abstract
Let f be a diffeomorphism of a closed C ∞ manifold M, and let Λ ⊂ M be a closed f-invariant set. We show that if f |Λ is robustly chain transitive with orbital shadowing property, then Λ is a basic set.
Acknowledgements
The authors wish to express their appreciation to the referee for his careful reading of the manuscript and valuable suggestions. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) and funded by the Ministry of Education, Science and Technology (No. 2011-0007649).