How restrictive is topological dynamics?
Commentationes Mathematicae Universitatis Carolinae (1997)
- Volume: 38, Issue: 3, page 563-569
- ISSN: 0010-2628
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topIwanik, Anzelm. "How restrictive is topological dynamics?." Commentationes Mathematicae Universitatis Carolinae 38.3 (1997): 563-569. <http://eudml.org/doc/248111>.
@article{Iwanik1997,
abstract = {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 $\{\mathbf \{Z\}\}^2$-actions without periodic points.},
author = {Iwanik, Anzelm},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {abstract dynamical system; pointwise periodic system; symbolic dynamics; $\mathbf \{Z\}^2$-action; abstract dynamical system; pointwise periodic system; symbolic dynamics; -action},
language = {eng},
number = {3},
pages = {563-569},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {How restrictive is topological dynamics?},
url = {http://eudml.org/doc/248111},
volume = {38},
year = {1997},
}
TY - JOUR
AU - Iwanik, Anzelm
TI - How restrictive is topological dynamics?
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 3
SP - 563
EP - 569
AB - 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 ${\mathbf {Z}}^2$-actions without periodic points.
LA - eng
KW - abstract dynamical system; pointwise periodic system; symbolic dynamics; $\mathbf {Z}^2$-action; abstract dynamical system; pointwise periodic system; symbolic dynamics; -action
UR - http://eudml.org/doc/248111
ER -
References
top- Edelstein M., On the representation of mappings of compact metrizable spaces as restrictions of linear transformations, Canad. J. Math 22 (1970), 372-375. (1970) Zbl0195.24604MR0263040
- Iwanik A., Period structure for pointwise periodic isometries of continua, Acta Univ. Carolin. - Math. Phys. 29 2 (1988), 19-21. (1988) Zbl0674.54020MR0983446
- 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. Zbl0696.54028MR0934109
- Janos L., Compactification and linearization of abstract dynamical systems, preprint. Zbl0928.54036MR1489853
- Kowalski Z.S., A characterization of periods in equicontinuous topological dynamical systems, Bull. Polish Ac. Sc. 38 (1990), 121-124. (1990) Zbl0769.54044MR1194254
- de Vries H., Compactification of a set which is mapped onto itself, Bull. Acad. Polon. Sci. 5 (1957), 943-945. (1957) Zbl0078.04202MR0092144
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