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David Pokluda

Characterization of

ω

-limit sets of continuous maps of the circle

Comment.Math.Univ.Carolinae 43,3 (2002) 575-581.

Abstract: In this paper we extend results of Blokh, Bruckner, Humke and Sm´ıtal [Trans. Amer. Math. Soc. 348 (1996), 1357–1372] about characterization ofω-limit sets from the classC(I, I) of continuous maps of the interval to the classC(S,S) of continuous maps of the circle. Among others we give geometric characterization of ω-limit sets and then we prove that the family ofω-limit sets is closed with respect to the Hausdorff metric.

Keywords: dynamical system, circle map,ω-limit set

AMS Subject Classification: Primary 37E10, 37B99, 26A18

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