Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber
We consider step and soft skew products over the Bernoulli shift which have an -dimensional closed manifold as a fiber. It is assumed that the fiber maps Hölder continuously depend on a point in the base. We prove that, in the space of skew product maps with this property, there exists an open domai...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/539736 |
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| author | Fatemeh Helen Ghane Mahboubeh Nazari Mohsen Saleh Zahra Shabani |
| author_facet | Fatemeh Helen Ghane Mahboubeh Nazari Mohsen Saleh Zahra Shabani |
| author_sort | Fatemeh Helen Ghane |
| collection | DOAJ |
| description | We consider step and soft skew products over the Bernoulli shift which have an -dimensional closed manifold as a fiber. It is assumed that the fiber maps Hölder continuously depend on a point in the base. We prove that, in the space of skew product maps with this property, there exists an open domain such that maps from this open domain have dense sets of periodic points that are attracting and repelling along the fiber. Moreover, robust properties of invariant sets of diffeomorphisms, including the
coexistence of dense sets of periodic points with different indices, are obtained. |
| format | Article |
| id | doaj-art-e22c0c1b207946db96a9774d46e0b3f8 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e22c0c1b207946db96a9774d46e0b3f82025-02-03T01:28:41ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/539736539736Robust Density of Periodic Orbits for Skew Products with High Dimensional FiberFatemeh Helen Ghane0Mahboubeh Nazari1Mohsen Saleh2Zahra Shabani3Department of Mathematics, Ferdowsi University of Mashhad, Mashhad 91775-1159, IranDepartment of Mathematics, Ferdowsi University of Mashhad, Mashhad 91775-1159, IranDepartment of Mathematics, University of Neyshabur, Neyshabur 93137 66835, IranDepartment of Mathematics, Ferdowsi University of Mashhad, Mashhad 91775-1159, IranWe consider step and soft skew products over the Bernoulli shift which have an -dimensional closed manifold as a fiber. It is assumed that the fiber maps Hölder continuously depend on a point in the base. We prove that, in the space of skew product maps with this property, there exists an open domain such that maps from this open domain have dense sets of periodic points that are attracting and repelling along the fiber. Moreover, robust properties of invariant sets of diffeomorphisms, including the coexistence of dense sets of periodic points with different indices, are obtained.http://dx.doi.org/10.1155/2013/539736 |
| spellingShingle | Fatemeh Helen Ghane Mahboubeh Nazari Mohsen Saleh Zahra Shabani Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber Abstract and Applied Analysis |
| title | Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber |
| title_full | Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber |
| title_fullStr | Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber |
| title_full_unstemmed | Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber |
| title_short | Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber |
| title_sort | robust density of periodic orbits for skew products with high dimensional fiber |
| url | http://dx.doi.org/10.1155/2013/539736 |
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