Cylinder cocycle extensions of minimal rotations on monothetic groups
Volume 101 / 2004
Colloquium Mathematicum 101 (2004), 75-88
MSC: Primary 54H20.
DOI: 10.4064/cm101-1-5
Abstract
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.
