Li-Yorke Sensitivity of Set-Valued Discrete Systems
Consider the surjective, continuous map f:X→X and the continuous map f¯ of 𝒦(X) induced by f, where X is a compact metric space and 𝒦(X) is the space of all nonempty compact subsets of X endowed with the Hausdorff metric. In this paper, we give a short proof that if f¯ is Li-Yoke sensitive, then f...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/260856 |
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| author | Heng Liu Fengchun Lei Lidong Wang |
| author_facet | Heng Liu Fengchun Lei Lidong Wang |
| author_sort | Heng Liu |
| collection | DOAJ |
| description | Consider the surjective, continuous map f:X→X and the continuous map f¯ of 𝒦(X) induced by f, where X is a compact metric space and 𝒦(X) is the space of all nonempty compact subsets of X endowed with the Hausdorff metric. In this paper, we give a short proof that if f¯ is Li-Yoke sensitive, then f is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of f does not imply Li-Yorke sensitivity of f¯. |
| format | Article |
| id | doaj-art-aeeb03172bdf40d7a0acc965ee16c94f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-aeeb03172bdf40d7a0acc965ee16c94f2025-02-03T06:05:50ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/260856260856Li-Yorke Sensitivity of Set-Valued Discrete SystemsHeng Liu0Fengchun Lei1Lidong Wang2Department of Mathematics, Dalian University of Technology, Dalian, Liaoning 116600, ChinaDepartment of Mathematics, Dalian University of Technology, Dalian, Liaoning 116600, ChinaDepartment of Mathematics, Dalian Nationalities University, Dalian, Liaoning 116600, ChinaConsider the surjective, continuous map f:X→X and the continuous map f¯ of 𝒦(X) induced by f, where X is a compact metric space and 𝒦(X) is the space of all nonempty compact subsets of X endowed with the Hausdorff metric. In this paper, we give a short proof that if f¯ is Li-Yoke sensitive, then f is Li-Yorke sensitive. Furthermore, we give an example showing that Li-Yorke sensitivity of f does not imply Li-Yorke sensitivity of f¯.http://dx.doi.org/10.1155/2013/260856 |
| spellingShingle | Heng Liu Fengchun Lei Lidong Wang Li-Yorke Sensitivity of Set-Valued Discrete Systems Journal of Applied Mathematics |
| title | Li-Yorke Sensitivity of Set-Valued Discrete Systems |
| title_full | Li-Yorke Sensitivity of Set-Valued Discrete Systems |
| title_fullStr | Li-Yorke Sensitivity of Set-Valued Discrete Systems |
| title_full_unstemmed | Li-Yorke Sensitivity of Set-Valued Discrete Systems |
| title_short | Li-Yorke Sensitivity of Set-Valued Discrete Systems |
| title_sort | li yorke sensitivity of set valued discrete systems |
| url | http://dx.doi.org/10.1155/2013/260856 |
| work_keys_str_mv | AT hengliu liyorkesensitivityofsetvalueddiscretesystems AT fengchunlei liyorkesensitivityofsetvalueddiscretesystems AT lidongwang liyorkesensitivityofsetvalueddiscretesystems |