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On groups of essential values of topological cylinder cocycles over minimal rotations

100%

Mentzen M.

Colloquium Mathematicum

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2003

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tom 95

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nr 2

241-253

EN

A theory of essential values of cocycles over minimal rotations with values in locally compact Abelian groups, especially $ℝ^m$, is developed. Criteria for such a cocycle to be conservative are given. The group of essential values of a cocycle is described.

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Cylinder cocycle extensions of minimal rotations on monothetic groups

63%

Mentzen M., Siemaszko A.

Colloquium Mathematicum

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2004

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tom 101

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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

Semisimple extensions of irrational rotations

51%

Lemańczyk M., Mentzen M., Nakada H.

Studia Mathematica

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2003

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tom 156

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nr 1

31-57

EN

We show that semisimple actions of l.c.s.c. Abelian groups and cocycles with values in such groups can be used to build new examples of semisimple automorphisms (ℤ-actions) which are relatively weakly mixing extensions of irrational rotations.

Ograniczanie wyników

2 Colloquium Mathematicum

1 Studia Mathematica

3 Mentzen M.

1 Lemańczyk M.

1 Nakada H.

1 Siemaszko A.

1 2004

2 2003

On groups of essential values of topological cylinder cocycles over minimal rotations

Cylinder cocycle extensions of minimal rotations on monothetic groups

Semisimple extensions of irrational rotations