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Relations between Shadowing and Inverse Shadowing in Dynamical Systems

Faculty of Mathematics and Mechanics, Saint-Petersburg State University, 198504 Saint Petersburg, Russia
Axioms 2019, 8(1), 11; https://doi.org/10.3390/axioms8010011
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)
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
MDPI and ACS Style

Petrov, A.A. Relations between Shadowing and Inverse Shadowing in Dynamical Systems. Axioms 2019, 8, 11. https://doi.org/10.3390/axioms8010011

AMA Style

Petrov AA. Relations between Shadowing and Inverse Shadowing in Dynamical Systems. Axioms. 2019; 8(1):11. https://doi.org/10.3390/axioms8010011

Chicago/Turabian Style

Petrov, Alexey A. 2019. "Relations between Shadowing and Inverse Shadowing in Dynamical Systems" Axioms 8, no. 1: 11. https://doi.org/10.3390/axioms8010011

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