Periodic shadowing and $\Omega$-stability

2010, Volume 15, Numbers 2-3, pp. 404-417

Author(s): Osipov A. V., Pilyugin S. Y., Tikhomirov S. B.

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, Volume 15, Numbers 2-3, pp. 404-417

DOI: 10.1134/S1560354710020255

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