# Relatively minimal extensions of topological flows

Colloquium Mathematicae (2000)

- Volume: 84/85, Issue: 1, page 51-65
- ISSN: 0010-1354

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topMentzen, Mieczysław. "Relatively minimal extensions of topological flows." Colloquium Mathematicae 84/85.1 (2000): 51-65. <http://eudml.org/doc/210808>.

@article{Mentzen2000,

abstract = {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.},

author = {Mentzen, Mieczysław},

journal = {Colloquium Mathematicae},

keywords = {factors; flows; topological dynamics},

language = {eng},

number = {1},

pages = {51-65},

title = {Relatively minimal extensions of topological flows},

url = {http://eudml.org/doc/210808},

volume = {84/85},

year = {2000},

}

TY - JOUR

AU - Mentzen, Mieczysław

TI - Relatively minimal extensions of topological flows

JO - Colloquium Mathematicae

PY - 2000

VL - 84/85

IS - 1

SP - 51

EP - 65

AB - 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.

LA - eng

KW - factors; flows; topological dynamics

UR - http://eudml.org/doc/210808

ER -

## References

top- [1] J. Aaronson, M. Lemańczyk, C. Mauduit and H. Nakada, Koksma's inequality and group extensions of Kronecker transformations, in: Algorithms, Fractals, and Dynamics, Plenum Press, New York, 1995, 27-50. Zbl0878.28009
- [2] R. Ellis, Lectures on Topological Dynamics, Benjamin, New York, 1969.
- [3] S. Glasner and B. Weiss, On the construction of minimal skew products, Israel J. Math. 34 (1979), 321-336. Zbl0434.54032
- [4] M. Lemańczyk and K. K. Mentzen, Topological ergodicity of real cocycles over minimal rotations, preprint. Zbl1002.54023
- [5] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, MacMillan of India, 1977. Zbl0421.28017
- [6] J. de Vries, Elements of Topological Dynamics, Kluwer Acad. Publ., 1993. Zbl0783.54035

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