Discrete orbits in topologically transitive cylindrical transformations

Jan Kwiatkowski; Artur Siemaszko

doi:10.3934/dcds.2010.27.945

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2010, Volume 27, Issue 3: 945-961. Doi: 10.3934/dcds.2010.27.945

This issue Previous Article Baire category and extremely non-normal points of invariant sets of IFS's Next Article On the distribution of periodic orbits

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
2.
Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. Żołnierska 14A, 10-561 Olsztyn

Received: March 31, 2009

Revised: January 31, 2010

Published: August 2010

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Abstract

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.

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Mathematics Subject Classification: 54H20.

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