David Pokluda
Characterization of $\omega $-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\'{\i }tal [Trans. Amer. Math. Soc. {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.

Keywords: dynamical system, circle map, $\omega $-limit set
AMS Subject Classification: Primary 37E10, 37B99, 26A18