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.
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.