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August  2010, 27(3): 945-961. doi: 10.3934/dcds.2010.27.945

Discrete orbits in topologically transitive cylindrical transformations

Jan Kwiatkowski 1, and  Artur Siemaszko 2,

1. 

Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
2. 

Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. Żołnierska 14A, 10-561 Olsztyn, Poland

Received  April 2009 Revised  February 2010 Published  March 2010

In this paper we provide a few recipes how to construct a topologically transitive cocycle over an arbitrary odometer possessing discrete orbits. It is shown that for every odometer, there exists a topologically transitive cocycle such that the set of points with discrete orbits starting form zero level has the cardinality of the continuum.
Keywords: cocycle group extension, cocycle, topological dynamics, minimal set, discrete orbits., cylinder transformation.
Mathematics Subject Classification: 54H2.
Citation: Jan Kwiatkowski, Artur Siemaszko. Discrete orbits in topologically transitive cylindrical transformations. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 945-961. doi: 10.3934/dcds.2010.27.945
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