Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
Czasopismo
Rocznik
Tom
Numer
Strony
51-65
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-05-04
poprawiono
1999-08-20
Twórcy
autor
- 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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv84i1p51bwm