A. V. Osipov, S. Yu. Pilyugin, S. B. Tikhomirov, “Periodic shadowing and $\Omega$-stability”, Regul. Chaotic Dyn., 15:2-3 (2010), 404

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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. Osipov^a, S. Yu. Pilyugin^a, S. B. Tikhomirov^b

^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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https://www.mathnet.ru/eng/rcd/v15/i2/p404

This publication is cited in the following 5 articles:

Citing articles in Google Scholar: Russian citations, English citations
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