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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 539736, 7 pages
http://dx.doi.org/10.1155/2013/539736
Research Article

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

1Department of Mathematics, Ferdowsi University of Mashhad, Mashhad 91775-1159, Iran
2Department of Mathematics, University of Neyshabur, Neyshabur 93137 66835, Iran

Received 2 June 2013; Revised 13 August 2013; Accepted 9 September 2013

Academic Editor: Ondřej Došlý

Copyright © 2013 Fatemeh Helen Ghane et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.