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On group extensions of 2-fold simple ergodic actions

100%
Siemaszko A.
Studia Mathematica
|
1994
|
tom 110
|
nr 1
53-64
EN
Compact group extensions of 2-fold simple actions of locally compact second countable amenable groups are considered. It is shown what the elements of the centralizer of such a system look like. It is also proved that each factor of such a system is determined by a compact subgroup in the centralizer of a normal factor.
2
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Cylinder cocycle extensions of minimal rotations on monothetic groups

63%
Mentzen M., Siemaszko A.
Colloquium Mathematicum
|
2004
|
tom 101
|
nr 1
75-88
EN
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.
3
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Extreme Relations for Topological Flows

51%
Kamiński B., Siemaszko A., Szymański J.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2005
|
tom 53
|
nr 1
17-24
EN
We introduce the concept of an extreme relation for a topological flow as an analogue of the extreme measurable partition for a measure-preserving transformation considered by Rokhlin and Sinai, and we show that every topological flow has such a relation for any invariant measure. From this result, it follows, among other things, that any deterministic flow has zero topological entropy and any flow which is a K-system with respect to an invariant measure with full support is a topological K-flow.
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