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Axioms 2018, 7(1), 18; https://doi.org/10.3390/axioms7010018

A Type of the Shadowing Properties for Generic View Points

Department of Mathematics, Mokwon University, Daejeon 302-729, Korea
Received: 15 November 2017 / Revised: 12 March 2018 / Accepted: 19 March 2018 / Published: 20 March 2018
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Abstract

We show that if a C 1 generic diffeomorphism of a closed smooth two-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it is Anosov. Moreover, if a C 1 generic vector field of a closed smooth three-dimensional manifold has the average shadowing property or the asymptotic average shadowing property, then it satisfies singular Axiom A without cycles. View Full-Text
Keywords: average shadowing; asymptotic average shadowing; generic; chain transitive; Axiom A; singular Axiom A; Anosov average shadowing; asymptotic average shadowing; generic; chain transitive; Axiom A; singular Axiom A; Anosov
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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Lee, M. A Type of the Shadowing Properties for Generic View Points. Axioms 2018, 7, 18.

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