1Faculty of Mathematics and Computer Science Nicolaus Copernicus University Chopina 12/18 87-100 Toruń, Poland 2Faculty of Mathematics and Information Technology University of Warmia and Mazury in Olsztyn Żołnierska 14A 10-561 Olsztyn, Poland
Colloquium Mathematicum, Tome 101 (2004) no. 1, pp. 75-88
The main results of this paper are:1. No topologically transitive cocycle
$\mathbb{R}^m$-extension of minimal rotation on the
unit circle by a continuous real-valued
bounded variation $\mathbb{Z}$-cocycle
admits minimal
subsets.2. A minimal rotation on a compact metric monothetic group does
not admit a topologically transitive
real-valued cocycle if and only if the
group is finite.
Keywords:
main results paper topologically transitive cocycle mathbb m extension minimal rotation unit circle continuous real valued bounded variation mathbb cocycle admits minimal subsets minimal rotation compact metric monothetic group does admit topologically transitive real valued cocycle only group finite
Affiliations des auteurs :
Mieczysław K. Mentzen
1
;
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 Information Technology University of Warmia and Mazury in Olsztyn Żołnierska 14A 10-561 Olsztyn, Poland
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author = {Mieczys{\l}aw K. Mentzen and Artur Siemaszko},
title = {Cylinder cocycle extensions of
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Mieczysław K. Mentzen; Artur Siemaszko. Cylinder cocycle extensions of
minimal rotations on monothetic groups. Colloquium Mathematicum, Tome 101 (2004) no. 1, pp. 75-88. doi: 10.4064/cm101-1-5
