Abstract
We show that a linear homeomorphism with the shadowing property of a Banach space is hyperbolic if and only if the set of points with bounded orbit is closed. The proof is based on an auxiliary type of shadowing called bounded shadowing property. We give examples where our result can be applied.
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Acknowledgements
Our gratitude to the members of the Dynamical Systems Seminar of the Department of Mathematics of the Chungnam National University, Daejeon, Republic of Korea, where the results of this paper were discussed. We also thank the anonymous referees for their important observations.
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KL and CAM were partially supported by NRF Grant No. 2018R1A2B3001457.
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Lee, K., Morales, C.A. Hyperbolicity, Shadowing, and Bounded Orbits. Qual. Theory Dyn. Syst. 21, 61 (2022). https://doi.org/10.1007/s12346-022-00588-9
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DOI: https://doi.org/10.1007/s12346-022-00588-9