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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| Format: | article |
| Langue: | EN |
| Publié: |
De Gruyter
2021
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| Accès en ligne: | https://doaj.org/article/9aa5ca6a2b624e2f8e21e80c1e2aa86a |
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| Résumé: | 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. |
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