| Title:
|
How restrictive is topological dynamics? (English) |
| Author:
|
Iwanik, A. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
563-569 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $T$ be a permutation of an abstract set $X$. In ZFC, we find a necessary and sufficient condition it terms of cardinalities of the $T$-orbits that allows us to topologize $(X,T)$ as a topological dynamical system on a compact Hausdorff space. This extends an early result of H. de Vries concerning compact metric dynamical systems. An analogous result is obtained for ${\bold Z}^2$-actions without periodic points. (English) |
| Keyword:
|
abstract dynamical system |
| Keyword:
|
pointwise periodic system |
| Keyword:
|
symbolic dynamics |
| Keyword:
|
$\bold Z^2$-action |
| MSC:
|
54H20 |
| idZBL:
|
Zbl 0938.54036 |
| idMR:
|
MR1485077 |
| . |
| Date available:
|
2009-01-08T18:36:17Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118954 |
| . |
| Reference:
|
Edelstein M.: On the representation of mappings of compact metrizable spaces as restrictions of linear transformations.Canad. J. Math 22 (1970), 372-375. Zbl 0195.24604, MR 0263040 |
| Reference:
|
Iwanik A.: Period structure for pointwise periodic isometries of continua.Acta Univ. Carolin. - Math. Phys. 29 2 (1988), 19-21. Zbl 0674.54020, MR 0983446 |
| Reference:
|
Iwanik A., Janos L., Kowalski Z.: Periods in equicontinuous topological dynamical systems.in: Nonlinear Analysis, Th. M. Rassias Ed., World Scientific Publ. Co. Singapore, 1987, pp.355-365. Zbl 0696.54028, MR 0934109 |
| Reference:
|
Janos L.: Compactification and linearization of abstract dynamical systems.preprint. Zbl 0928.54036, MR 1489853 |
| Reference:
|
Kowalski Z.S.: A characterization of periods in equicontinuous topological dynamical systems.Bull. Polish Ac. Sc. 38 (1990), 121-124. Zbl 0769.54044, MR 1194254 |
| Reference:
|
de Vries H.: Compactification of a set which is mapped onto itself.Bull. Acad. Polon. Sci. 5 (1957), 943-945. Zbl 0078.04202, MR 0092144 |
| . |
