| Title:
|
Characterization of $\omega$-limit sets of continuous maps of the circle (English) |
| Author:
|
Pokluda, David |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
575-581 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we extend results of Blokh, Bruckner, Humke and Sm'{\i}tal [Trans. Amer. Math. Soc. {\bf 348} (1996), 1357--1372] about characterization of $\omega$-limit sets from the class $\Cal{C}(I,I)$ of continuous maps of the interval to the class $\Cal C(\Bbb S,\Bbb S)$ of continuous maps of the circle. Among others we give geometric characterization of $\omega$-limit sets and then we prove that the family of $\omega$-limit sets is closed with respect to the Hausdorff metric. (English) |
| Keyword:
|
dynamical system |
| Keyword:
|
circle map |
| Keyword:
|
$\omega$-limit set |
| MSC:
|
26A18 |
| MSC:
|
37B99 |
| MSC:
|
37E10 |
| idZBL:
|
Zbl 1090.37027 |
| idMR:
|
MR1920533 |
| . |
| Date available:
|
2009-01-08T19:25:20Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119347 |
| . |
| Reference:
|
[1] Alsedà L., Llibre J., Misiurewicz M.: Combinatorial Dynamics and Entropy in Dimension One.World Scientific Publ., Singapore, 1993. MR 1255515 |
| Reference:
|
[2] Block L.S., Coppel W.A.: Dynamics in One Dimension.Lecture Notes in Math. 1513, Springer, Berlin, 1992. Zbl 0746.58007, MR 1176513 |
| Reference:
|
[3] Blokh A., Bruckner A.M., Humke P.D., Smítal J.: The space of $ømega $-limit sets of a continuous map of the interval.Trans. Amer. Math. Soc. 348 (1996), 1357-1372. MR 1348857 |
| 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, pp. 3-9 (Russian). Zbl 0605.58007, MR 0884346 |
| Reference:
|
[5] Hric R.: Topological sequence entropy for maps of the circle.Comment. Math. Univ. Carolinae 41 (2000), 53-59. Zbl 1039.37007, MR 1756926 |
| Reference:
|
[6] Pokluda D.: On the transitive and $ømega$-limit points of the continuous mappings of the circle.Archivum Mathematicum, accepted for publication. Zbl 1087.37033 |
| Reference:
|
[7] Sharkovsky A.N.: The partially ordered system of attracting sets.Soviet Math. Dokl. 7 5 (1966), 1384-1386. |
| . |
