C2-Stably Limit Shadowing Diffeomorphisms
Let f be a diffeomorphism on a C∞ closed surface. In this paper, we show that if f has the C2-stably limit shadowing property, then we have the following: (i) f satisfies the Kupka-Smale condition; (ii) if P(f) is dense in the nonwandering set Ω(f) and if there is a dominated splitting on Ps(f), the...
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Hindawi Limited
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/751769 |
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doaj-51bf5bff914548a0bc47976238d0515c2020-11-24T23:02:07ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/751769751769C2-Stably Limit Shadowing DiffeomorphismsManseob Lee0Junmi Park1Department of Mathematics, Mokwon University, Daejeon 302-729, Republic of KoreaDepartment of Mathematics, Chungnam National University, Daejeon 305-764, Republic of KoreaLet f be a diffeomorphism on a C∞ closed surface. In this paper, we show that if f has the C2-stably limit shadowing property, then we have the following: (i) f satisfies the Kupka-Smale condition; (ii) if P(f) is dense in the nonwandering set Ω(f) and if there is a dominated splitting on Ps(f), then f satisfies both Axiom A and the strong transversality condition.http://dx.doi.org/10.1155/2015/751769 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Manseob Lee Junmi Park |
| spellingShingle |
Manseob Lee Junmi Park C2-Stably Limit Shadowing Diffeomorphisms Abstract and Applied Analysis |
| author_facet |
Manseob Lee Junmi Park |
| author_sort |
Manseob Lee |
| title |
C2-Stably Limit Shadowing Diffeomorphisms |
| title_short |
C2-Stably Limit Shadowing Diffeomorphisms |
| title_full |
C2-Stably Limit Shadowing Diffeomorphisms |
| title_fullStr |
C2-Stably Limit Shadowing Diffeomorphisms |
| title_full_unstemmed |
C2-Stably Limit Shadowing Diffeomorphisms |
| title_sort |
c2-stably limit shadowing diffeomorphisms |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2015-01-01 |
| description |
Let f be a diffeomorphism on a C∞ closed surface. In this paper, we show that if f has the C2-stably limit shadowing property, then we have the following: (i) f satisfies the Kupka-Smale condition; (ii) if P(f) is dense in the nonwandering set Ω(f) and if there is a dominated splitting on Ps(f), then f satisfies both Axiom A and the strong transversality condition. |
| url |
http://dx.doi.org/10.1155/2015/751769 |
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AT manseoblee c2stablylimitshadowingdiffeomorphisms AT junmipark c2stablylimitshadowingdiffeomorphisms |
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