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Relatively minimal extensions of topological flows

100%
Mentzen M. K.
Colloquium Mathematicum
|
2000
|
tom 84/85
|
nr 1
51-65
EN
The concept of relatively minimal (rel. min.) extensions of topological flows is introduced. Several generalizations of properties of minimal extensions are shown. In particular the following extensions are rel. min.: distal point transitive, inverse limits of rel. min., superpositions of rel. min. Any proximal extension of a flow Y with a dense set of almost periodic (a.p.) points contains a unique subflow which is a relatively minimal extension of Y. All proximal and distal factors of a point transitive flow with a dense set of a.p. points are rel. min. In the class of point transitive flows with a dense set of a.p. points, distal open extensions are disjoint from all proximal extensions. An example of a relatively minimal point transitive extension determined by a cocycle which is a coboundary in the measure-theoretic sense is given.
2
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Automorphisms with finite exact uniform rank

100%
Mentzen M. K.
Studia Mathematica
|
1991
|
tom 100
|
nr 1
13-24
EN
The notion of exact uniform rank, EUR, of an automorphism of a probability Lebesgue space is defined. It is shown that each ergodic automorphism with finite EUR is finite extension of some automorphism with rational discrete spectrum. Moreover, for automorphisms with finite EUR, the upper bounds of EUR of their factors and ergodic iterations are computed.
3
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Ergodic properties of group extensions of dynamical systems with discrete spectra

100%
Mentzen M. K.
Studia Mathematica
|
1991-1992
|
tom 101
|
nr 1
19-31
EN
Ergodic group extensions of a dynamical system with discrete spectrum are considered. The elements of the centralizer of such a system are described. The main result says that each invariant sub-σ-algebra is determined by a compact subgroup in the centralizer of a normal natural factor.
4
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Invariant sub-σ-algebras for substitutions of constant length

44%
Mentzen M. K.
Studia Mathematica
|
1989
|
tom 92
|
nr 3
257-273
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