| Title:
|
On the transitive and $\omega$-limit points of the continuous mappings of the circle (English) |
| Author:
|
Pokluda, David |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
49-52 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend the recent results from the class $\mathcal {C}(I,I)$ of continuous maps of the interval to the class $\mathcal {C}(\mathbb {S},\mathbb {S})$ of continuous maps of the circle. Among others, we give a characterization of $\omega $-limit sets and give a characterization of sets of transitive points for these maps. (English) |
| MSC:
|
37B25 |
| MSC:
|
37E10 |
| idZBL:
|
Zbl 1087.37033 |
| idMR:
|
MR1899567 |
| . |
| Date available:
|
2008-06-06T22:29:47Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107818 |
| . |
| Reference:
|
[1] Agronsky S. J., Bruckner A. M., Ceder J. G., Pearson T. L.: The structure of $\omega $-limit sets for continuous functions.Real Anal. Exchange 15 (1989/1990), 483–510. MR 1059418 |
| Reference:
|
[2] Alsedà L., Llibre J., Misiurewicz M.: Combinatorial Dynamics and Entropy in Dimension One.World Scientific Publ., Singapore 1993. MR 1255515 |
| Reference:
|
[3] Block L. S., Coppel W. A.: Dynamics in One Dimension.Lecture Notes in Math., vol. 1513, Springer, Berlin, 1992. Zbl 0746.58007, MR 1176513 |
| Reference:
|
[4] Blokh A. M.: On transitive mappings of one-dimensional ramified manifolds.in Differential-difference equations and problems of mathematical physics, Inst. Mat. Acad. Sci., Kiev, 1984, 3–9 (Russian). Zbl 0605.58007, MR 0884346 |
| Reference:
|
[5] Kolyada S., Snoha, L’.: Some aspects of topological transitivity – a survey.Iteration Theory (ECIT 94), Grazer Math. Ber. 334 (1997), 3–37. Zbl 0907.54036, MR 1644768 |
| Reference:
|
[6] Pokluda D., Smítal J.: A “universal” dynamical system generated by a continuous map of the interval.Proc. Amer. Math. Soc. 128 (2000), 3047–3056. Zbl 0973.37025, MR 1712885 |
| Reference:
|
[7] Pokluda D.: On the structure of sets of transitive points for continuous maps of the interval.Real Anal. Exchange, 25 (1999/2000), 45–48. |
| . |
