Title:

Characterization of $\omega$limit sets of continuous maps of the circle (English) 
Author:

Pokluda, David 
Language:

English 
Journal:

Commentationes Mathematicae Universitatis Carolinae 
ISSN:

00102628 (print) 
ISSN:

12137243 (online) 
Volume:

43 
Issue:

3 
Year:

2002 
Pages:

575581 
. 
Category:

math 
. 
Summary:

In this paper we extend results of Blokh, Bruckner, Humke and Sm'{\i}tal [Trans. Amer. Math. Soc. {\bf 348} (1996), 13571372] 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:

20090108T19:25:20Z 
Last updated:

20120430 
Stable URL:

http://hdl.handle.net/10338.dmlcz/119347 
. 
Reference:

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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), 13571372. MR 1348857 
Reference:

[4] Blokh A.M.: On transitive mappings of onedimensional ramified manifolds.in Differentialdifference Equations and Problems of Mathematical Physics, Inst. Mat. Acad. Sci., Kiev, 1984, pp. 39 (Russian). Zbl 0605.58007, MR 0884346 
Reference:

[5] Hric R.: Topological sequence entropy for maps of the circle.Comment. Math. Univ. Carolinae 41 (2000), 5359. 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), 13841386. 
. 