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ABSTRACT
Let f be a diffeomorphism on a compact smooth Riemannian manifold M, and let Λ be a closed f-invariant transitive subset of M. In this paper, we show that f|Λ is C1-stably expansive if and only if Λ is a hyperbolic basic set. Moreover, C1-generically, a locally maximal transitive set Λ is expansive if and only if it is a hyperbolic basic set.
Acknowledgments
The author thanks the referee for the careful reading and helpful comments that improved the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
This work is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning [grant number 2014R1A1A1A05002124].