A Type of the Shadowing Properties for Generic View Points

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 a...

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Bibliographic Details
Main Author:	Manseob Lee
Format:	Article
Language:	English
Published:	MDPI AG 2018-03-01
Series:	Axioms
Subjects:	average shadowing asymptotic average shadowing generic chain transitive Axiom A singular Axiom A Anosov
Online Access:	http://www.mdpi.com/2075-1680/7/1/18

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spelling	doaj-b14d273543e041d7b016ff3b5b103e462020-11-24T22:29:39ZengMDPI AGAxioms2075-16802018-03-01711810.3390/axioms7010018axioms7010018A Type of the Shadowing Properties for Generic View PointsManseob Lee0Department of Mathematics, Mokwon University, Daejeon 302-729, KoreaWe 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.http://www.mdpi.com/2075-1680/7/1/18average shadowingasymptotic average shadowinggenericchain transitiveAxiom Asingular Axiom AAnosov
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Manseob Lee
spellingShingle	Manseob Lee A Type of the Shadowing Properties for Generic View Points Axioms average shadowing asymptotic average shadowing generic chain transitive Axiom A singular Axiom A Anosov
author_facet	Manseob Lee
author_sort	Manseob Lee
title	A Type of the Shadowing Properties for Generic View Points
title_short	A Type of the Shadowing Properties for Generic View Points
title_full	A Type of the Shadowing Properties for Generic View Points
title_fullStr	A Type of the Shadowing Properties for Generic View Points
title_full_unstemmed	A Type of the Shadowing Properties for Generic View Points
title_sort	type of the shadowing properties for generic view points
publisher	MDPI AG
series	Axioms
issn	2075-1680
publishDate	2018-03-01
description	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.
topic	average shadowing asymptotic average shadowing generic chain transitive Axiom A singular Axiom A Anosov
url	http://www.mdpi.com/2075-1680/7/1/18
work_keys_str_mv	AT manseoblee atypeoftheshadowingpropertiesforgenericviewpoints AT manseoblee typeoftheshadowingpropertiesforgenericviewpoints
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A Type of the Shadowing Properties for Generic View Points

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