Abstract
We show that the following three properties of a diffeomorphism f of a smooth closed manifold are equivalent: (i) f belongs to the C 1-interior of the set of diffeomorphisms having the periodic shadowing property; (ii) f has the Lipschitz periodic shadowing property; (iii) f is Ω-stable.
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The research of the first author is supported by the German-Russian Interdisciplinary Science Center (G-RISC) financed by the German Academic Exchange Service (DAAD). The research of the third author is supported by NSC (Taiwan) 98-2811-M-002-061.
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Osipov, A.V., Pilyugin, S.Y. & Tikhomirov, S.B. Periodic shadowing and Ω-stability. Regul. Chaot. Dyn. 15, 404–417 (2010). https://doi.org/10.1134/S1560354710020255
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DOI: https://doi.org/10.1134/S1560354710020255