Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space
This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map space, which consists of continuous maps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem, it is shown that the map space contains a dense set of maps...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/520273 |
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| _version_ | 1832563463285637120 |
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| author | Qiuju Xing Yuming Shi |
| author_facet | Qiuju Xing Yuming Shi |
| author_sort | Qiuju Xing |
| collection | DOAJ |
| description | This paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map space, which consists of continuous maps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem, it is shown that the map space contains a dense set of maps that have transversal homoclinic orbits and are chaotic in the sense of both Li-Yorke and Devaney with positive topological entropy. |
| format | Article |
| id | doaj-art-e9b5a84388d845b0a3aea3b4c7700512 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e9b5a84388d845b0a3aea3b4c77005122025-02-03T01:20:14ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/520273520273Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map SpaceQiuju Xing0Yuming Shi1Department of Mathematics, Shandong University, Jinan, Shandong 250100, ChinaDepartment of Mathematics, Shandong University, Jinan, Shandong 250100, ChinaThis paper is concerned with distribution of maps with transversal homoclinic orbits in a continuous map space, which consists of continuous maps defined in a closed and bounded set of a Banach space. By the transversal homoclinic theorem, it is shown that the map space contains a dense set of maps that have transversal homoclinic orbits and are chaotic in the sense of both Li-Yorke and Devaney with positive topological entropy.http://dx.doi.org/10.1155/2011/520273 |
| spellingShingle | Qiuju Xing Yuming Shi Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space Abstract and Applied Analysis |
| title | Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space |
| title_full | Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space |
| title_fullStr | Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space |
| title_full_unstemmed | Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space |
| title_short | Distribution of Maps with Transversal Homoclinic Orbits in a Continuous Map Space |
| title_sort | distribution of maps with transversal homoclinic orbits in a continuous map space |
| url | http://dx.doi.org/10.1155/2011/520273 |
| work_keys_str_mv | AT qiujuxing distributionofmapswithtransversalhomoclinicorbitsinacontinuousmapspace AT yumingshi distributionofmapswithtransversalhomoclinicorbitsinacontinuousmapspace |