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Article

A Type of the Shadowing Properties for Generic View Points

Department of Mathematics, Mokwon University, Daejeon 302-729, Korea
Axioms 2018, 7(1), 18; https://doi.org/10.3390/axioms7010018
Submission received: 15 November 2017 / Revised: 12 March 2018 / Accepted: 19 March 2018 / Published: 20 March 2018
(This article belongs to the Special Issue Shadowing in Dynamical Systems)

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.
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

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MDPI and ACS Style

Lee, M. A Type of the Shadowing Properties for Generic View Points. Axioms 2018, 7, 18. https://doi.org/10.3390/axioms7010018

AMA Style

Lee M. A Type of the Shadowing Properties for Generic View Points. Axioms. 2018; 7(1):18. https://doi.org/10.3390/axioms7010018

Chicago/Turabian Style

Lee, Manseob. 2018. "A Type of the Shadowing Properties for Generic View Points" Axioms 7, no. 1: 18. https://doi.org/10.3390/axioms7010018

APA Style

Lee, M. (2018). A Type of the Shadowing Properties for Generic View Points. Axioms, 7(1), 18. https://doi.org/10.3390/axioms7010018

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