Cylinder cocycle extensions of minimal rotations on monothetic groups

Mieczysław K. Mentzen, and Artur Siemaszko. "Cylinder cocycle extensions of minimal rotations on monothetic groups." Colloquium Mathematicae 101.1 (2004): 75-88. <http://eudml.org/doc/283831>.

@article{MieczysławK2004,
abstract = {The main results of this paper are: 1. No topologically transitive cocycle $ℝ^m$-extension of minimal rotation on the unit circle by a continuous real-valued bounded variation 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.},
author = {Mieczysław K. Mentzen, Artur Siemaszko},
journal = {Colloquium Mathematicae},
keywords = {topological dynamics; cocycles; minimal sets; cylinder transformations},
language = {eng},
number = {1},
pages = {75-88},
title = {Cylinder cocycle extensions of minimal rotations on monothetic groups},
url = {http://eudml.org/doc/283831},
volume = {101},
year = {2004},
}

TY - JOUR
AU - Mieczysław K. Mentzen
AU - Artur Siemaszko
TI - Cylinder cocycle extensions of minimal rotations on monothetic groups
JO - Colloquium Mathematicae
PY - 2004
VL - 101
IS - 1
SP - 75
EP - 88
AB - The main results of this paper are: 1. No topologically transitive cocycle $ℝ^m$-extension of minimal rotation on the unit circle by a continuous real-valued bounded variation 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.
LA - eng
KW - topological dynamics; cocycles; minimal sets; cylinder transformations
UR - http://eudml.org/doc/283831
ER -