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2013
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# Sergey Pilyugin

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

## Publications:

 Osipov A. V., Pilyugin S. Y., Tikhomirov S. B. Periodic shadowing and $\Omega$-stability 2010, vol. 15, no. 2-3, pp.  404-417 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 Citation: Osipov A. V., Pilyugin S. Y., Tikhomirov S. B.,  Periodic shadowing and $\Omega$-stability, Regular and Chaotic Dynamics, 2010, vol. 15, no. 2-3, pp. 404-417 DOI:10.1134/S1560354710020255
 Pilyugin S. Y. Transversality and local inverse shadowing 2006, vol. 11, no. 2, pp.  311-318 Abstract The inverse shadowing property of a dynamical system means that, given a family of approximate trajectories, for any real trajectory we can find a close approximate trajectory from the given family. This property is of interest when we study dynamical systems numerically. In this paper, we describe some relations between the transversality of a heteroclinic trajectory of a diffeomorphism and the local inverse shadowing property for this heteroclinic trajectory. Keywords: shadowing, heteroclinic trajectory, transversality Citation: Pilyugin S. Y.,  Transversality and local inverse shadowing , Regular and Chaotic Dynamics, 2006, vol. 11, no. 2, pp. 311-318 DOI: 10.1070/RD2006v011n02ABEH000354