Relatively minimal extensions of topological flows

• Autorzy: Mieczysław K. Mentzen
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

factors; flows; topological dynamics

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 1
• Strony: 51-65

Daty

wydano

2000

otrzymano

1999-05-04

poprawiono

1999-08-20

Twórcy

autor

Mieczysław K. Mentzen

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [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.
• [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.
• [4] M. Lemańczyk and K. K. Mentzen, Topological ergodicity of real cocycles over minimal rotations, preprint.
• [5] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, MacMillan of India, 1977.
• [6] J. de Vries, Elements of Topological Dynamics, Kluwer Acad. Publ., 1993.