We study the C 1-interiors of sets of diffeomorphisms of a closed smooth manifold with various limit shadowing properties. It is shown that, for some natural analogs of the usual limit shadowing property, the corresponding C 1-interiors coincide with the set of Ω-stable diffeomorphisms. The same problem is considered for two-sided analogs of the limit shadowing property.
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To Pavol Brunovsky on the occasion of his 70th birthday.
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Pilyugin, S.Y. Sets of Dynamical Systems with Various Limit Shadowing Properties. J Dyn Diff Equat 19, 747–775 (2007). https://doi.org/10.1007/s10884-007-9073-2
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DOI: https://doi.org/10.1007/s10884-007-9073-2