A. V. Osipov, S. Yu. Pilyugin, S. B. Tikhomirov, “Periodic shadowing and <nobr>$\Omega$</nobr>-stability”, Regul. Chaotic Dyn., 2010, Volume 15, Issue 2-3,Pages <nobr>404

This article is cited 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

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.

MSC: 37C50, 37D20

Received: 27.11.2009
Accepted: 29.12.2009

Language: English