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Sergey Pilyugin

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


Osipov A. V., Pilyugin S. Y., Tikhomirov S. B.
Periodic shadowing and $\Omega$-stability
2010, vol. 15, no. 2-3, pp.  404-417
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
Pilyugin S. Y.
Transversality and local inverse shadowing
2006, vol. 11, no. 2, pp.  311-318
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

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