Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber | Zendy

F.H. Ghane | Zendy; Mahboubeh Nazari | Zendy; M. Saleh | Zendy; Zahra Shabani | Zendy

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Robust Density of Periodic Orbits for Skew Products with High Dimensional Fiber

Author(s) -

F.H. Ghane,

Mahboubeh Nazari,

M. Saleh,

Zahra Shabani

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/539736

Subject(s) - mathematics , combinatorics , skew , product (mathematics) , fiber , base (topology) , manifold (fluid mechanics) , domain (mathematical analysis) , mathematical analysis , geometry , physics , composite material , mechanical engineering , astronomy , engineering , materials science

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 thecoexistence of dense sets of periodic points with different indices, are obtained

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