Asymptotic measure-expansiveness for generic diffeomorphisms

In this paper, we will assume MM to be a compact smooth manifold and f:M→Mf:M\to M to be a diffeomorphism. We herein demonstrate that a C1{C}^{1} generic diffeomorphism ff is Axiom A and has no cycles if ff is asymptotic measure expansive. Additionally, for a C1{C}^{1} generic diffeomorphism ff, if...

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Autor principal:	Lee Manseob
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	expansive measure expansive asymptotic measure expansive generic axiom a homoclinic class hyperbolic 37c20 37d20 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/9aa5ca6a2b624e2f8e21e80c1e2aa86a
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id	oai:doaj.org-article:9aa5ca6a2b624e2f8e21e80c1e2aa86a
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spelling	oai:doaj.org-article:9aa5ca6a2b624e2f8e21e80c1e2aa86a2021-12-05T14:10:53ZAsymptotic measure-expansiveness for generic diffeomorphisms2391-545510.1515/math-2021-0037https://doaj.org/article/9aa5ca6a2b624e2f8e21e80c1e2aa86a2021-06-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0037https://doaj.org/toc/2391-5455In this paper, we will assume MM to be a compact smooth manifold and f:M→Mf:M\to M to be a diffeomorphism. We herein demonstrate that a C1{C}^{1} generic diffeomorphism ff is Axiom A and has no cycles if ff is asymptotic measure expansive. Additionally, for a C1{C}^{1} generic diffeomorphism ff, if a homoclinic class H(p,f)H\left(\hspace{0.08em}p,f) that contains a hyperbolic periodic point pp of ff is asymptotic measure-expansive, then H(p,f)H\left(\hspace{0.08em}p,f) is hyperbolic of ff.Lee ManseobDe Gruyterarticleexpansivemeasure expansiveasymptotic measure expansivegenericaxiom ahomoclinic classhyperbolic37c2037d20MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 470-476 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	expansive measure expansive asymptotic measure expansive generic axiom a homoclinic class hyperbolic 37c20 37d20 Mathematics QA1-939
spellingShingle	expansive measure expansive asymptotic measure expansive generic axiom a homoclinic class hyperbolic 37c20 37d20 Mathematics QA1-939 Lee Manseob Asymptotic measure-expansiveness for generic diffeomorphisms
description	In this paper, we will assume MM to be a compact smooth manifold and f:M→Mf:M\to M to be a diffeomorphism. We herein demonstrate that a C1{C}^{1} generic diffeomorphism ff is Axiom A and has no cycles if ff is asymptotic measure expansive. Additionally, for a C1{C}^{1} generic diffeomorphism ff, if a homoclinic class H(p,f)H\left(\hspace{0.08em}p,f) that contains a hyperbolic periodic point pp of ff is asymptotic measure-expansive, then H(p,f)H\left(\hspace{0.08em}p,f) is hyperbolic of ff.
format	article
author	Lee Manseob
author_facet	Lee Manseob
author_sort	Lee Manseob
title	Asymptotic measure-expansiveness for generic diffeomorphisms
title_short	Asymptotic measure-expansiveness for generic diffeomorphisms
title_full	Asymptotic measure-expansiveness for generic diffeomorphisms
title_fullStr	Asymptotic measure-expansiveness for generic diffeomorphisms
title_full_unstemmed	Asymptotic measure-expansiveness for generic diffeomorphisms
title_sort	asymptotic measure-expansiveness for generic diffeomorphisms
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/9aa5ca6a2b624e2f8e21e80c1e2aa86a
work_keys_str_mv	AT leemanseob asymptoticmeasureexpansivenessforgenericdiffeomorphisms
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Asymptotic measure-expansiveness for generic diffeomorphisms

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