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Regular and Chaotic Dynamics, 2010, Volume 15, Issue 2-3, Pages 404–417 (Mi rcd505)  
This article is cited in 5 scientific papers (total in 5 papers)

On the 75th birthday of Professor L.P. Shilnikov

Periodic shadowing and $\Omega$-stability

A. V. Osipova, S. Yu. Pilyugina, S. B. Tikhomirovb

a Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetsky pr. 28, St. Petersburg, 198504 Russia
b Dept. of Math., National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan 10617
Citations (5)
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 $\Omega$-stable.
Keywords: periodic shadowing, hyperbolicity, $\Omega$-stability.
Received: 27.11.2009
Accepted: 29.12.2009
Document Type: Personalia
MSC: 37C50, 37D20
Language: English
Citation: A. V. Osipov, S. Yu. Pilyugin, S. B. Tikhomirov, “Periodic shadowing and $\Omega$-stability”, Regul. Chaotic Dyn., 15:2-3 (2010), 404–417
Citation in format AMSBIB
\Bibitem{OsiPilTik10}
\by A. V. Osipov, S. Yu. Pilyugin, S. B. Tikhomirov
\paper Periodic shadowing and $\Omega$-stability
\jour Regul. Chaotic Dyn.
\yr 2010
\vol 15
\issue 2-3
\pages 404--417
\mathnet{http://mi.mathnet.ru/rcd505}
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    • This publication is cited in the following 5 articles:
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