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Axioms 2019, 8(1), 11; https://doi.org/10.3390/axioms8010011

Relations between Shadowing and Inverse Shadowing in Dynamical Systems

Faculty of Mathematics and Mechanics, Saint-Petersburg State University, 198504 Saint Petersburg, Russia
Received: 15 December 2018 / Revised: 13 January 2019 / Accepted: 15 January 2019 / Published: 17 January 2019
(This article belongs to the Special Issue Shadowing in Dynamical Systems)
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Abstract

In this paper, we study relations between shadowing and inverse shadowing for homeomorphisms of a compact space. We present an example of a smooth diffeomorphism of a compact three-dimensional manifold that has the shadowing property and does not have the inverse shadowing property. For some classes of inverse shadowing, we construct examples of homeomorphisms that have the inverse shadowing property but do not have the shadowing property. View Full-Text
Keywords: shadowing property; inverse shadowing property; axiom A; structural stability; strong transversality condition; C0-transversality condition shadowing property; inverse shadowing property; axiom A; structural stability; strong transversality condition; C0-transversality condition
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Petrov, A.A. Relations between Shadowing and Inverse Shadowing in Dynamical Systems. Axioms 2019, 8, 11.

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