Cylinder cocycle extensions of
minimal rotations on monothetic groups

Mieczysław K. Mentzen; Artur Siemaszko

doi:10.4064/cm101-1-5

Geodesic

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Cylinder cocycle extensions of minimal rotations on monothetic groups

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

Colloquium Mathematicum, Tome 101 (2004) no. 1, pp. 75-88.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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.

DOI : 10.4064/cm101-1-5

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

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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. http://geodesic.mathdoc.fr/articles/10.4064/cm101-1-5/

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