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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:
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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 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
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