Aleksei Osipov

prosp. Gagarina, 23, korp. 4, 198504, St. Petersburg, Russian
Faculty of Mathematics and Mechanics, St. Petersburg State University


Osipov A. V., Pilyugin S. Y., Tikhomirov S. B.
Periodic shadowing and $\Omega$-stability
2010, vol. 15, nos. 2-3, pp.  404-417
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 $\Omega$-stable.
Keywords: periodic shadowing, hyperbolicity, $\Omega$-stability
Citation: Osipov A. V., Pilyugin S. Y., Tikhomirov S. B.,  Periodic shadowing and $\Omega$-stability, Regular and Chaotic Dynamics, 2010, vol. 15, nos. 2-3, pp. 404-417

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