Robustly shadowable chain transitive sets and hyperbolicity
We say that a compact invariant set Λ of a C 1 -vector field X on a compact boundaryless Riemannian manifold M is robustly shadowable if it is locally maximal with respect to a neighbourhood U of Λ, and there exists a C 1 -neighbourhood of X such that for any , the continuation Λ Y of Λ for Y and U...
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| Veröffentlicht in: | Dynamical systems (London, England) England), 2018-10, Vol.33 (4), p.602-621 |
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| container_title | Dynamical systems (London, England) |
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| creator | Bagherzad, Mohammad Reza Lee, Keonhee |
| description | We say that a compact invariant set Λ of a C
1
-vector field X on a compact boundaryless Riemannian manifold M is robustly shadowable if it is locally maximal with respect to a neighbourhood U of Λ, and there exists a C
1
-neighbourhood
of X such that for any
, the continuation Λ
Y
of Λ for Y and U is shadowable for Y
t
. In this paper, we prove that any chain transitive set of a C
1
-vector field on M is hyperbolic if and only if it is robustly shadowable. |
| doi_str_mv | 10.1080/14689367.2017.1417355 |
| format | Article |
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1
-vector field X on a compact boundaryless Riemannian manifold M is robustly shadowable if it is locally maximal with respect to a neighbourhood U of Λ, and there exists a C
1
-neighbourhood
of X such that for any
, the continuation Λ
Y
of Λ for Y and U is shadowable for Y
t
. In this paper, we prove that any chain transitive set of a C
1
-vector field on M is hyperbolic if and only if it is robustly shadowable.</description><identifier>ISSN: 1468-9367</identifier><identifier>EISSN: 1468-9375</identifier><identifier>DOI: 10.1080/14689367.2017.1417355</identifier><language>eng</language><publisher>Abingdon: Taylor & Francis</publisher><subject>Chain transitive sets ; Chains ; dominated splitting ; hyperbolicity ; Production planning ; Riemann manifold ; robustly shadowing</subject><ispartof>Dynamical systems (London, England), 2018-10, Vol.33 (4), p.602-621</ispartof><rights>2018 Informa UK Limited, trading as Taylor & Francis Group 2018</rights><rights>2018 Informa UK Limited, trading as Taylor & Francis Group</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c286t-f64ab4470f141839c206f8b991443719184431c2a7b0eaaf0aa6167f61ea306b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27903,27904</link.rule.ids></links><search><creatorcontrib>Bagherzad, Mohammad Reza</creatorcontrib><creatorcontrib>Lee, Keonhee</creatorcontrib><title>Robustly shadowable chain transitive sets and hyperbolicity</title><title>Dynamical systems (London, England)</title><description>We say that a compact invariant set Λ of a C
1
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1
-neighbourhood
of X such that for any
, the continuation Λ
Y
of Λ for Y and U is shadowable for Y
t
. In this paper, we prove that any chain transitive set of a C
1
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1
-vector field X on a compact boundaryless Riemannian manifold M is robustly shadowable if it is locally maximal with respect to a neighbourhood U of Λ, and there exists a C
1
-neighbourhood
of X such that for any
, the continuation Λ
Y
of Λ for Y and U is shadowable for Y
t
. In this paper, we prove that any chain transitive set of a C
1
-vector field on M is hyperbolic if and only if it is robustly shadowable.</abstract><cop>Abingdon</cop><pub>Taylor & Francis</pub><doi>10.1080/14689367.2017.1417355</doi><tpages>20</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1468-9367 |
| ispartof | Dynamical systems (London, England), 2018-10, Vol.33 (4), p.602-621 |
| issn | 1468-9367 1468-9375 |
| language | eng |
| recordid | cdi_proquest_journals_2126462965 |
| source | Business Source Complete |
| subjects | Chain transitive sets Chains dominated splitting hyperbolicity Production planning Riemann manifold robustly shadowing |
| title | Robustly shadowable chain transitive sets and hyperbolicity |
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