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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| Format: | Article |
| Language: | English |
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Wiley
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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| _version_ | 1832556065222295552 |
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| author | Manseob Lee Junmi Park |
| author_facet | Manseob Lee Junmi Park |
| author_sort | Manseob Lee |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-51bf5bff914548a0bc47976238d0515c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-51bf5bff914548a0bc47976238d0515c2025-02-03T05:46:25ZengWileyAbstract 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 |
| spellingShingle | Manseob Lee Junmi Park C2-Stably Limit Shadowing Diffeomorphisms Abstract and Applied Analysis |
| title | 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_short | C2-Stably Limit Shadowing Diffeomorphisms |
| title_sort | c2 stably limit shadowing diffeomorphisms |
| url | http://dx.doi.org/10.1155/2015/751769 |
| work_keys_str_mv | AT manseoblee c2stablylimitshadowingdiffeomorphisms AT junmipark c2stablylimitshadowingdiffeomorphisms |